Physics Lab

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temple university physics

Mapping the Electrostatic Potential and Electric Field

The objective of this experiment is to study the potentials, equipotential curves and electric fields produced by various two-dimensional electrostatic charge distributions. In practice, direct measurement of the electric field turns out to be quite difficult. Instead, we exploit the fact that the electric force is a conservative force, and thus can be considered to be associated with a potential – the electric potential , where the components of the electric field vector are given by the change of the electric potential in that direction,

    (1)

One consequence of Equation 1 is that if one can identify a line (or surface) along which the potential has a constant value then the electric field is necessarily perpendicular to that line at all points, see Figure 1. Therefore, in order to map the electric field for a charge configuration, it is sufficient to map out the equipotential lines.

There is a technical difficulty, however, with setting up and controlling static charge distributions: it is not easy to fix charges at precise locations. For this reason we will simulate static charge distributions using a small direct current flowing through electrodes, drawn to look like our static charge distributions, and conducting paper. The electric field shapes, potential and equipotential lines will be identical to those for the simulated static charge configurations.

Figure 1. Equipotentials and electric field lines for a positive point charge (circle at center).

 

NOTE: You may want to reference your text or other sources to confirm your results and aid in mapping the fields accurately and expeditiously.

 

 

 

Learning Goals for this Laboratory:

· Practice visualizing electric fields and electric potentials around conductors of many shapes.

· Practice graphing and analyzing nonlinear relations.

· Practice connecting simple circuits.

 

Apparatus

Pasco field mapping board, digital voltage meter with point probes, D.C. power supply, several sheets of conducting paper with different electrode configurations, push pins

 

Figure 2. Setup for Part IV of this lab showing the cork board with the parallel plate electrode configuration on conducting paper, voltmeter and D.C. power supply.

 

 

Part I. Point Source and Guard Ring

Figure 3. Point source and ring guard configuration. Voltmeter probes not shown.

 

1. The electrodes in this experiment are made with conducting silver paint on conductive paper. Locate the conductive paper with the point source and guard ring electrode configuration (Figure 3) and pin the corners of the paper to the cork board.

2. Take a cable with a banana plug on one end and a ring terminal on the other and plug the banana end into the positive of the power supply, then pin the ring terminal end of the cable into the central point electrode using a metal pushpin as in Figure 3. Make sure there is good contact between the ring terminal and the painted electrode. Try to avoid making new holes in the electrode with the pushpin, it is sufficient to have physical contact between the terminal of the wire lead and the silver of the electrode.

3. Similarly, connect the negative of the power supply with the circle-shaped guard ring electrode.

4. Turn on the power supply and set it to 5 V by first increasing the current limit knob, then increasing the voltage to 5 V. This voltage provides a continuous source of charge to the electrodes, creating the electric field and potential we will measure.

5. Before measuring the field and potential, let’s check the electrodes for proper conductivity (a damaged electrode could skew your results).

If the electrode is a good conductor, all points on the electrode should have nearly the same potential. For our purposes, the maximum potential between any two points on a single electrode should not be more than a few mV. Use the voltmeter to probe the potential between different points along an electrode. Please do not push the voltmeter probes through the paper; simply placing the probes on the paper should give you a good reading. If you see a potential larger than a few mV between different points on an electrode, first check that the power supply wires are firmly connected to the electrode via the pushpin. If you still see a potential where there shouldn’t be one the electrodes could be damaged, so ask your lab instructor to double-check your setup and get a replacement electrode if necessary.

6. Once you’ve checked for good conductivity, you’re ready to measure the potential of the point source. Place the black (common) voltmeter probe on the guard ring so that it is the reference, and use the red probe to measure the voltage starting at the point 2 mm from the edge of the point source and ending 20 mm from the point source at intervals of 2 mm. In this way, you will have 10 data points: 2, 4, 6, 8, and 10 mm from the point source. If it helps, you can use a pencil to mark the 2 mm points. The voltage at 2 mm should be somewhere in the 3 – 5 V range.

7. Make a graph of the potential as a function of distance from the point source (the edge of the point source is at = 0.0 cm, and = 5 V).

8. Make a second graph of potential vs. (do this by having Excel calculate in new column).

Question 1. According to theory, how does the potential of a point charge vary with distance as you move away from the point charge? Is this what your graph shows? For an ideal point source, the graph of potential vs. should be a line, is yours a line? Our point source is not ideal because the negative electrode is not infinitely far away. However, very near the point source the negative electrode is sufficiently far away as to have no influence, thus the first few points at higher voltage in the graph should follow a linear trend.

9. Mapping equipotential lines. Use the voltmeter to find equipotentials by keeping the black probe on the negative electrode and placing the red probe at a point somewhere inside the circle. Watch the voltmeter voltage reading while you slide the red probe along the paper while also trying to keep the voltage constant. This line of constant potential is an equipotential. Try doing this for one or two other values of potential nearer and farther from the point source.

Question 2. What are the shapes of the equipotentials in the region around a point source? Do your results agree with the equipotentials show in Figure 1?

10. Briefly survey the potential in the region outside the guard ring.

Question 3. Does the potential vary much from one point to another outside of the guard ring? What does this imply about the electric field outside the guard ring? Refer to equation 1 for help with your answer.

Part II. Electric Dipole

1. Replace the point source electrode with the electric dipole configuration and connect the leads to the 5 V source as in Fig. 4, making sure the pushpins provide good contact between the ring terminal and the silver paint.

Figure 4. Dipole configuration. Voltmeter probes not shown.

 

2. Place the black reference voltage probe halfway between the two electrodes, we’ll keep it fixed at this location. Place the red probe somewhere on the paper. Then slide the red probe along the paper while watching the voltage reading. Use this method to map out several equipotential curves nearer and farther from the point charges. Record your results on the white grid paper provided. To see what the shape should be in theory, refer to online or text sources for the potential of a dipole.

3. After drawing several equipotentials on your grid paper, use a different color to draw in the corresponding electric field lines. To do this, start at the positive charge and draw a line moving outward such that it crosses any equipotential lines at right angles. The electric field lines should terminate at the negative charge. Be sure to indicate the direction of your e-field with arrows along the lines. To see what the shape of these field lines should be, refer to online or text sources for the electric field of a dipole. Once you have several field lines drawn, take a picture of the resulting map of electric field and potential for your lab report.

Question 4. Note all but one of the equipotential lines for a dipole are curved. Where is the uniquely straight equipotential line for a dipole?

Part III. Like Charges in a Box

1. Set up the configuration shown in Fig. 5 and apply 5 V. Note that the two point charges are positive, you can use a wire to daisy-chain them together so they are both charged. Also note that the box electrode surrounding the point charges is negative. As in Part II, place your reference voltage probe halfway between the two electrodes.

Question 5. Relative to this halfway point, where on the conducting paper is the potential highest? Where is it lowest?

Figure 5. Like Charges in a Box. Voltmeter probes not shown.

 

2. As you did with the dipole, map out a few equipotential lines near the point charges and also near the walls of the box. Make a rough map of these equipotentials and their corresponding E-field and include it with your lab report.

Part IV. Parallel Plates

Figure 6. Parallel plate electrodes (blue lines) connected to power supply. Voltmeter probes not shown.

The potential and field in between charged parallel plates differs significantly from that of a point source (Part I).

1. Connect the parallel plate electrodes to a power supply as shown. Measure the potential every 0.5 cm along a line from the midpoint of the negative electrode to the midpoint of the positive electrode (i.e. along the dotted line in the figure at right). Use the negative electrode as the fixed reference for your measurement.

2. Make a graph of the potential as a function of distance from one plate (the reference probe is at = 0.0 cm).

Question 6. Referring to your graph, describe in how the potential changes with distance from the electrode. How does this contrast to the potential vs distance for a point source you found in Part I?

For Your Lab Report:

Refer to the lab syllabus and grading rubric for what to include in the report. It may be helpful to use the answers to the questions to aid in writing the discussion.

 

 

1

6/28/20 3:46:00 PM

 
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Physics Word Problems

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Answer the following problems.

1. Pistons are fitted to two cylindrical chambers connected through a horizontal tube to form a hydraulic system. The piston chambers and the connecting tube are filled with an incompressible fluid. The cross-sectional areas of piston 1 and piston 2 are A1 and A2, respectively. A force F1 is exerted on piston 1. Rank the resultant force F2 on piston 2 that results from the combinations of F1, A1, and A2 given from greatest to smallest. If any of the combinations yield the same force, give them the same ranking. (Use only “>” or “=” symbols. Do not include any parentheses around the letters or symbols.)

  1. F1 = 6.0 N; A1 = 1.1 m2; and A2 = 2.2 m2
  2. F1 = 3.0 N; A1 = 1.1 m2; and A2 = 0.55 m2
  3. F1 = 3.0 N; A1 = 2.2 m2; and A2 = 4.4 m2
  4. F1 = 6.0 N; A1 = 0.55 m2; and A2 = 2.2 m2
  5. F1 = 6.0 N; A1 = 0.55 m2; and A2 = 1.1 m2
  6. F1 = 3.0 N; A1 = 2.2 m2; and A2 = 1.1 m2

2. A bicycle tire pump has a piston with area 0.49 in2. If a person exerts a force of 24 lb on the piston while inflating a tire, what pressure does this produce on the air in the pump?
psi=

3. A large truck tire is inflated to a gauge pressure of 82 psi. The total area of one sidewall of the tire is 1,330 in2. What is the net outward force (in lb) on the sidewall because of the air pressure? (Enter the magnitude.)

lb=

4. A viewing window on the side of a large tank at a public aquarium measures 59 in. by 69 in. The average gauge pressure from the water is 7 psi. What is the total outward force on the window?
lb=

5. The total mass of the hydrogen gas in the Hindenburg zeppelin was 18,000 kg. What volume did the hydrogen occupy? (Assume that the temperature of the hydrogen was 0°C and that it was at a pressure of 1 atm.)
m3=

6. A large balloon used to sample the upper atmosphere is filled with 590 m3 of hydrogen. What is the mass of the hydrogen (in kg)?

kg=

7. Find the gauge pressure (in psi) at the bottom of a freshwater swimming pool that is 18.6 ft deep.

psi=

8. The depth of the Pacific Ocean in the Mariana Trench is 36,198 ft. What is the gauge pressure at this depth?
psi=

9. An ebony log with volume 15.0 ft3 is submerged in water. What is the buoyant force on it (in lb)? (Enter the magnitude.)

lb=

10. An empty storage tank has a volume of 9,490 ft3. What is the buoyant force exerted on it by the air? (Assume the air is at 0°C and 1 atm.)
lb=

11. A modern-day zeppelin holds 9,770 m3 of helium. Compute its maximum payload at sea level. (Assume the helium and air to be at 0°C and 1 atm.)
N=

12. A boat (with a flat bottom) and its cargo weigh 6,400 N. The area of the boat’s bottom is 5 m2. How far below the surface of the water is the boat’s bottom when it is floating in water?
m=

13. A scale reads 378 N when a piece of iron is hanging from it. What does it read (in N) when it is lowered so that the iron is submerged in water?

N=

14. A dentist’s chair with a person in it weighs 2000 N. The output plunger of a hydraulic system starts to lift the chair when the dental assistant’s foot exerts a force of 44 N on the input piston. Neglecting any difference in the heights of the piston and the plunger, what is the ratio of the area of the plunger to the area of the piston?

Aplunger/Apiston =

15. The wing of an airplane has an average cross-sectional area of 13 m2 and experiences a lift force of 91,000 N. What is the average difference in the air pressure between the top and bottom of the wing?
N/m2=

16. Air flows through a heating duct with a square cross-section with 9-inch sides at a speed of 4.1 ft/s. Just before reaching an outlet in the floor of a room, the duct widens to assume a square cross-section with sides equal to 15 inches. Compute the speed of the air flowing into the room (in ft/s), assuming that we can treat the air as an incompressible fluid.

ft/s=

17. A metal bowl with a weight of 1.45 N is placed in a larger kitchen container filled with olive oil. How much olive oil must the bowl displace in order to float? For reference, the mass density of olive oil is about 910 g/liter and its weight density is about 8.92 N/liter. Please give your answer in liters.

liters=

 
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Physics 226 Fall 2013 #Problem Set 1

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Physics 226 Fall 2013 #Problem Set 1

NOTE: Show ALL work and ALL answers on a piece of separate loose leaf paper, not on this sheet.

Due on Thursday, August 29th

1) Skid and Mitch are pushing on a sofa in opposite directions with forces of 530 N and 370 N respectively. The mass of the sofa is 48 kg. The sofa is initially at rest before it accelerates. There is no friction acting on the sofa. (a) Calculate the acceleration of the sofa. (b) What velocity does the sofa have after it moves 2.5 m? (c) How long does it take to travel 2.5 m?

2) You have three force

vectors acting on a mass at the origin. Use the component method we covered in lecture to find the magnitude and direction of the re- sultant force acting on the mass.

3) You have three force

vectors acting on a mass at the origin. Use the component method we covered in lecture to find the magnitude and direction of the re- sultant force acting on the mass.

4) A bowling ball rolls off of a table that is 1.5 m tall. The

ball lands 2.5 m from the base of the table. At what speed did the ball leave the table?

5) Skid throws his guitar up

into the air with a velocity of 45 m/s. Calculate the maximum height that the guitar reaches from the point at which Skid lets go of the guitar. Use energy methods.

6) A beam of mass 12 kg and length 2 m is attached to a

hinge on the left. A box of 80 N is hung from the beam 50 cm from the left end. You hold the beam horizontally with your obviously powerful index finger. With what force do you push up on the beam?

Mitch Sofa Skid

7) The tennis ball of mass 57 g which

you have hung in your garage that lets you know where to stop your car so you don’t crush your garbage cans is entertaining you by swinging in a vertical circle of radius 75 cm. At the bottom of its swing it has a speed of 4 m/s. What is the tension in the string at this point?

y

8) Derivatives:

a) Given: y = (4x + L)(2×2 – L), find dx dy

.

b) Given: Lx2 Lx2lny , find dx dy

.

9) Integrals:

a) Given: 45 45 dr cosk, evaluate.

b) Given:  R0 2322 dr xr kxr2 , evaluate.

ANSWERS:

 

1) a) 3.33 m/s2 b) 4.08 m/s c) 1.23 s 2) 48.0 N, 61.0º N of W 3) 27.4 N, 16.1º S of E 4) 4.52 m/s 5) 103.3 m 6) 78.8 N

7) 1.78N 8) a) 24×2 + 4xL – 4L

b) 22 x4L L4

 

9) a) r k2

b)

22 xR

x1k2

F2 = 90 N

F1 = 40 N 35

45 x

F3 = 60 N

y

F1 = 45 N 60

F2 = 65 N

50 x

70

F3 = 85 N

Guitar

Skid

 

 

Physics 226 Fall 2013

Problem Set #2

1) A plastic rod has a charge of –2.0 C. How many

electrons must be removed so that the charge on the rod becomes +3.0C?

–

+

+

+

2)

Three identical metal spheres, A, B, and C initially have net charges as shown. The “q” is just any arbitrary amount of charge. Spheres A and B are now touched together and then separated. Sphere C is then touched to sphere A and separated from it. Lastly, sphere C is touched to sphere B and then separated from it. (a) How much charge ends up on sphere C? What is the total charge on the three spheres (b) before they are allowed to touch each other and (c) after they have touched? (d) Explain the relevance of the answers to (b) and (c).

 

3)

Skid of 40 kg and Mitch of 60 kg are standing on ice on opposite sides of an infinite black pit. They are each carrying neutral massless spheres while standing 8 m apart. Suppose that 3.0 x 1015 electrons are removed from one sphere and placed on the other. (a) Calculate the magnitude of the electrostatic force on each sphere. Are the forces the same or different? Explain. (b) Calculate the magnitude of the accelerations for Skid and Mitch at the moment they are 8 m apart. Are they the same or different? Explain. (c) As Skid and Mitch move closer together do their accelerations increase, decrease, or remain the same? Explain.

4) An electron travels in a circular orbit around a stationary

proton (i.e. a hydrogen atom). In order to move in a circle there needs to be a centripetal force acting on the electron. This centripetal force is due to the electrostatic force between the electron and the proton. The electron has a kinetic energy of 2.18 x 10–18 J. (a) What is the speed of the electron? (b) What is the radius of orbit of the electron?

 

5)

Three charges are arranged as shown. From the left to the right the values of the charges are 6 μC, – 1.5 μC, and – 2 μC. Calculate the magnitude and direction of the net electrostatic force on the charge on the far left.

6) For the same charge distribution of Problem #5, calculate

the magnitude and direction of the net electrostatic force on the charge on the far right.

7)

Two charged spheres are connected to a spring as shown. The unstretched length of the spring is 14 cm. (a) With Qa = 6 μC and Qb = – 7 μC, the spring compresses to an equilibrium length of 10 cm. Calculate the spring constant. (b) Qb is now replaced with a different charge Qc. The spring now has an equilibrium length of 20 cm. What is the magnitude of the charge Qc? (c) What is the sign of Qc? How do you know this?

8) The two charges above are fixed and cannot move. Find

the location in between the charges that you could put a proton so that the proton would have a net force of zero.

9) Three charges are fixed to an xy coordinate system.

A charge of –12 C is on the y axis at y = +3.0 m. A charge of +18 C is at the origin. Lastly, a charge of + 45 C is on the x axis at x = +3.0 m. Calculate the magnitude and direction of the net electrostatic force on the charge x = +3.0 m.

10) Four charges are situated

at the corners of a square each side of length 18 cm. The charges have the same magnitude of q = 4 μC but different signs. See diagram. Find the magnitude and direction of the net force on lower right charge.

 

+5q – 1q Neutral

C B A

Skid Mitch

Infinite Black Pit

– –

3 cm 2 cm

+

– + Qa Qb

+

8 cm

+ 4 μC 12 μC

 

 

11) For the same charge distribution of problem #10, find the magnitude and direction of the net force on upper right charge.

 

20

12)

All the charges above are multiples of “q” where q = 1μC. The horizontal and vertical distances between the charges are 15 cm. Find the magnitude and direction of the net electric force on the center charge.

 

13) Use the same charge distribution as in problem #12 but change all even-multiple charges to the opposite sign. Find the magnitude and direction of the net electric force on center charge.

14) Two small metallic spheres, each

of mass 0.30 g, are suspended by light strings from a common point as shown. The spheres are given the same electric charge and it is found that the two come to equilibrium when the two strings have an angle of 20 between them. If each string is 20.0 cm long, what is the magnitude of the charge on each sphere?

– 4q +9q +4q

+3q +3q +8q

15)

+6q R2 – 4q 12 cm m A meter stick of 15 kg is suspended by a string at the

60 cm location. A mass, m, is hung at the 80 cm mark. A massless charged sphere of + 4 μC is attached to the meter stick at the left end. Below this charge is another charge that is fixed 12 cm from the other when the meter stick is horizontal. It has a charge of – 4 μC. Calculate the mass, m, so that the meter stick remains horizontal.

 

ANSWERS:

 

7) a) 945 N/m b) 4.2 x 10–5 C 8) 2.93 cm 9) 0.648 N, 17.2º 10) 4.06 N, 45º 11) 6.66 N, 64.5º 12) 19.69 N, 80.1º 13) 18.5 N, 23.4º 14) 1.67 x 10–8 C 15) 10.56 kg

1) 3.1 x 1013 e–

2) a) +1.5q b) +4q c) +4q 3) a) FE, Skid = 32.4 N b) aSkid = 0.81 m/s2 4) a) 2.19 x 106 m/s b) 5.27 x 10–11 m 5) FE = 133.2 N, → 6) FE = 24.3 N, →

 

 

Physics 226 Fall 2013

 

Problem Set #3 1) A charge of –1.5 C is placed on the x axis at

x = +0.55 m, while a charge of +3.5 C is placed at the origin. (a) Calculate the magnitude and direction of the net electric field on the x-axis at x = +0.8 m. (b) Determine the magnitude and direction of the force that would act on a charge of –7.0 C if it was placed on the x axis at x = +0.8 m.

 

 

2) For the same charge distribution of problem #1, do the

following. (a) Calculate the magnitude and direction of the net electric field on the x-axis at x = +0.4 m. (b) Determine the magnitude and direction of the force that would act on a charge of –7.0 C if it was placed on the x axis at x = +0.4 m.

3)

Charges are placed at the three corners of a rectangle as shown. The charge values are q1 = 6 nC, q2 = – 4 nC, and q3 = 2.5 nC. Calculate the magnitude and direction of the electric field at the fourth corner.

4) For the same charge distribution of problem #3, with the

exception that you change both q1 and q2 to the opposite sign, calculate the magnitude and direction of the electric field at the fourth corner.

5) A drop of oil has a mass of 7.5 x 10–8 kg and a charge of

– 4.8 nC. The drop is floating close the to Earth’s surface because it is in an electric field. (a) Calculate the magnitude and direction of the electric field. (b) If the sign of the charge is changed to positive, then what is the acceleration of the oil drop? (c) If the oil drop starts from rest, then calculate the speed of the oil drop after it has traveled 25 cm.

6) A proton accelerates from rest in a uniform electric field

of magnitude 700 N/C. At a later time, its speed is 1.8 x 106 m/s. (a) Calculate the acceleration of the proton. (b) How much time is needed for the proton to reach this speed? (c) How far has the proton traveled during this time? (d) What is the proton’s kinetic energy at this time?

 

7) All the charges above are multiples of “q” where

q = 1μC. The horizontal and vertical distances between the charges are 25 cm. Find the magnitude and direction of the net electric field at point P.

8) Use the same charge distribution as in problem #7 but

change all even-multiple charges to the opposite sign. Find the magnitude and direction of the net electric field at point P.

9) In the above two diagrams, M & S, an electron is given an

initial velocity, vo, of 7.3 x 106 m/s in an electric field of 50 N/C. Ignore gravitation effects. (a) In diagram M, how far does the electron travel before it stops? (b) In diagram S, how far does the electron move vertically after it has traveled 6 cm horizontally? (Hint: Think projectile motion)

 

– +

+ P

q3 q2

q1

35 cm

20 cm

– 8q

– 4q

+9q

+9q

– 5q

+6q +6q

+2q

P

– – vo vo

M S

 

 

10) A 2 g plastic sphere is suspended by a 25 cm long piece of string. Do not ignore gravity. The sphere is hanging in a uniform electric field of magnitude 1100 N/C. See diagram. If the sphere is in equilibrium when the string makes a 20 angle with the vertical, what is the magnitude and sign of the net charge on the sphere?

11) You have an electric dipole of

opposite charges q and distance 2a apart. (a) Find an equation in terms of q, a, and y for the magnitude of the total electric field for an electric dipole at any distance y away from it. (b) Find an equation in terms of q, a, and y for the magnitude of the total electric field for an electric dipole at a distance y away from it for when y >> a.

12)

A dipole has an electric dipole moment of magnitude 4 μC·m. Another charge, 2q, is located a distance, d, away from the center of the dipole. In the diagram all variables of q = 20 μC and d = 80 cm. Calculate the net force on the 2q charge.

 

 

13) An electric dipole of charge 30 μC and separation 60 mm is put in a uniform electric field of strength 4 x 106 N/C. What is the magnitude of the torque on the dipole in a uniform field when (a) the dipole is parallel to the field, (b) the dipole is perpendicular to the field, and (c) the dipole makes an angle of 30º to the field. 20º

14) An electron of charge, – e, and mass, m, and a positron of charge, e, and mass, m, are in orbit around each other. They are a distance, d, apart. The center of their orbit is halfway between them. (a) Name the force that is acting as the centripetal force making them move in a circle. (b) Calculate the speed, v, of each charge in terms of e, m, k (Coulomb’s Constant), and d.

15) A ball of mass, m, and positive charge, q, is dropped from

rest in a uniform electric field, E, that points downward. If the ball falls through a height, h, and has a velocity of

gh2v  , find its mass in terms of q, g, and E.

16) The two charges above are fixed and cannot move. Find a

point in space where the total electric field will equal zero.

 

ANSWERS:

 

1) a) 1.67 x 105 N/C, WEST

b) 1.17 N, EAST 2) a) 7.97 x 105 N/C, EAST b) 5.6 N, EAST 3) 516 N/C, 61.3º 4) 717 N/C, 69.8º 5) a) 153.1 N/C, SOUTH b) 19.6 m/s2

c) 3.13 m/s 6) a) 6.71 x 1010 m/s2

b) 2.68 x 10–5 s c) 24.1 m d) 2.71 x 10–15 J 7) 1.23 x 106 N/C, 80.5º 8) 3.06 x 105 N/C, 48.4º

9) a) 3.04 m b) 0.297 mm 10) 6.49 x 10–6 C

11) a)  222 ay kqay4

b) 3y kqa4

 

12) 5.81 N 13) a) 0 b) 7.2 N·m c) 3.6 N·m

14) md2 kev 

15) g

Eq m 

16) 8.2 cm

–

+ y q

a

a

–q +

6 cm

– – 4 μC 12 μC

d

– + – q q 2q

+

 

 

Physics 226 Fall 2013

 

Problem Set #4

NOTE: Any answers of zero must have some kind of justification. 1) You have a thin straight wire of

charge and a solid sphere of charge. The amount of charge on each object is 8 mC and it is uniformly spread over each object. The length of the wire and the diameter of the sphere are both 13 cm. (a) Find the amount of charge on 3.5 cm of the wire. (b) For the sphere, how much charge is located within a radius of 3.5 cm from its center?

2) A uniform line of charge with density, λ, and length, L

is positioned so that its center is at the origin. See diagram above. (a) Determine an equation (using integration) for the magnitude of the total electric field at point P a distance, d, away from the origin. (b) Calculate the magnitude and direction of the electric field at P if d = 2 m, L = 1 m, and λ = 5 μC/m. (c) Show that if d >> L then you get an equation for the E-field that is equivalent to what you would get for a point charge. (We did this kind of thing in lecture.)

 

 

3)

A uniform line of charge with charge, Q, and length, L, is positioned so that its center is at the left end of the line. See diagram above. (a) Determine an equation (using integration) for the magnitude of the x-component of the total electric field at point P a distance, d, above the left end of the line. (b) Calculate the magnitude and direction of the x-component of the total electric field at point P if d = 1.5 m, L = 2.5 m, and Q = – 8 μC. (c) What happens to your equation from part (a) if d >> L? Conceptually explain why this is true.

 

4)

13 cm

You have a semi-infinite line of charge with a uniform linear density 8 μC/m. (a) Calculate the magnitude of the total electric field a distance of 7 cm above the left end of line. (You can use modified results from lecture and this homework if you like … no integration necessary.) (b) At what angle will this total E-field act? (c) Explain why this angle doesn’t change as you move far away from the wire. Can you wrap your brain around why this would be so?

d

5)

 

 

A uniform line of charge with charge, Q, and length, D, is positioned so that its center is directly below point P which is a distance, d, above. See diagram above. (a) Determine the magnitude of the x-component of the total electric field at point P. You must explain your answer or show calculations. (b) Calculate the magnitude and direction of the y-component of the total electric field at P if d = 2 m, D = 4.5 m, and Q = –12 μC. HINT: You can use integration to do this OR you can use one of the results (equations) we got in lecture and adapt it to this problem.

6) You have an infinite line of charge of constant linear

density, λ. (a) Determine an equation for the magnitude of the total electric field at point P a distance, d, away from the origin. Use any method you wish (except Gauss’ Law) to determine the equation. There’s at least three different ways you could approach this. You can use the diagram in #5 where D →  if you want a visual. (b) Calculate the electric field at d = 4 cm with λ = 3 μC/m.

 

P + + + + + +

0 2 L

2 L

P

0

d

– – – – – – – L

P

0

7 cm

 + + + + +

P

d

– – – – – – – D

 

 

7)

You have three lines of charge each with a length of 50 cm. The uniform charge densities are shown. The horizontal distance between the left plate and right ones is 120 cm. Find the magnitude and direction of the TOTAL E-field at P which is in the middle of the left plate and the right ones.

8) For the same charge distribution of problem #7, with the

exception that you change the sign of the 4 μC plate and you change the distance between the plates to 160 cm, find the magnitude and direction of the TOTAL E-field at P which is in the middle of the left plate and the right ones.

9) You have 3 arcs of charge, two ¼ arcs and one ½ arc.

The arcs form of circle of radius 5 cm. The uniform linear densities are shown in the diagram. (a) Using an integral and showing your work, determine the equation for the electric field at point P due to the ½ arc. (b) Calculate the magnitude and direction of the total electric field at point P.

10) For this problem use the same charge distribution as

problem #9, with the exception of changing all even charges to the opposite sign. (a) Using an integral and showing your work, determine the equation for the electric field at point P due to the ½ arc. (b) Calculate the magnitude and direction of the total electric field at point P.

11) You have two thin discs both

of diameter 26 cm. They also have the same magnitude surface charge density of, 20 μC/m2, but opposite sign. The charge is uniformly distributed on the discs. The discs are parallel to each

other and are separated by a distance of 30 cm. (a) Calculate the magnitude and direction of the total electric field at a point halfway between the discs along their central axes. (b) Calculate the magnitude and direction of the total electric field at a point halfway between the discs along their central axes if the diameter of the discs goes to infinity. (c) Determine the total electric field at a point halfway between the discs along their central axes if discs have charge of the same sign.

– 5 μC/m

+ + + +

+ +

– – –

3 μC/m

4 μC/m

P

12) You have two concentric thin rings of

charge. The outer ring has a dia- meter of 50 cm with a uniformly spread charge of – 15 μC. The inner ring has a diameter of 22 cm with a uniform linear charge density of 15 μC/m. Calculate the magnitude and direction of the total E-field at point P which lies 40 cm away from the rings along their central axes.

P

13) A proton is released from rest 5 cm away from an infinite

disc with uniform surface charge density of 0.4 pC/m2. (a) What is the acceleration of the proton once it’s released? (b) Calculate the kinetic energy of the proton after 2.5 s. [See Conversion Sheet for metric prefixes.]

2 μC/m 14) In the above two diagrams, G & L, an electron is given

an initial velocity, vo, of 7.3 x 106 m/s above infinite discs with uniform surface charge density of –0.15 fC/m2. (a) In diagram G, how much time passes before the electron stops? (b) In diagram L, how far does the electron move horizontally after it has traveled 20 m vertically? (Hint: Think projectile motion)

15) Two thin infinite planes

of surface charge density 6 nC/cm2 intersect at 45º to each other. See the diagram in which the planes are coming out of the page (edge on view). Point P lies 15 cm from each plane. Calculate the magnitude and direction of the total electric field at P.

 

–

+ + +

– – +

– – 2 μC/m 5 μC/m

+

+

+

P – –

L G

vo vo

P

45º

P – +

 

 

ANSWERS:

 

 

1) a) 2.15 mC b) 1.25 mC

2) a) 22 Ld4 Lk4 

 b) 1.2 x 104 N/C,

 

 

 

 

 

EAST

3) a)  

 

 

22x Ld

d 1

dL Qk

E

b) 9322 N/C, EAST c) 0 4) a) 1.46 x 106 N/C b) 45º c) Because Ex = Ey 5) a) 0 b) 1.79 x 104 N/C, SOUTH 6) 1.35 x 106 N/C, NORTH

7) 5.93 x 104 N/C, 13.6º 8) 2.37 x 104 N/C, 59.8º

9) a) R k2Ey 

b) 4.85 x 105 N/C, 22.0º

10) a) R k2E y 

b) 2.05 x 106 N/C, 74.8º 11) a) 5.53 x 105 N/C, WEST b) 2.26 x 106 N/C, WEST c) 0 12) 1.01 x 105 N/C, WEST 13) a) 2.17 x 106 m/s2 b) 2.45 x 10–14 J 14) a) 4.9 s b) 3780 m 15) 2.6 x 106 N/C, 22.5º

 

 

Physics 226 Fall 2013

 

Problem Set #5

NOTE: Any answers of zero must have some kind of justification. 1)

A uniform electric field of strength 300 N/C at an angle of 30º with respect to the x-axis goes through a cube of sides 5 cm. (a) Calculate the flux through each cube face: Front, Back, Left, Right, Top, and Bottom. (b) Calculate the net flux through the entire surface. (c) An electron is placed centered 10 cm from the left surface. What is the net flux through the entire surface? Explain your answer.

2)

A right circular cone of height 25 cm and radius 10 cm is enclosing an electron, centered 12 cm up from the base. See Figure G. (a) Using integration and showing all work, find the net flux through the cone’s surface. The electron is now centered in the base of the cone. See Figure L. (b) Calculate the net flux through the surface of the cone.

3) Using the cube in #1, you place a 4μC charge directly in the center of the cube. What is the flux through the top face? (Hint: Consider that this problem would be MUCH more difficult if the charge was not centered in the cube.)

4) Using the cube in #1, you place a 4μC charge at the lower,

left, front corner. What is the net flux through the cube? (Hint: Think symmetry.)

5) You have a thin spherical shell

of radius 10 cm with a uni- form surface charge density of – 42 μC/m2. Centered inside the sphere is a point charge of 4 μC. Find the magnitude and direction of the total electric field at: (a) r = 6 cm and (b) r = 12 cm.

6) You have a solid sphere of radius 6 cm and uniform volume charge density of – 6 mC/m3. Enclosing this is a thin spherical shell of radius 10 cm with a total charge of 7 μC that is uniformly spread over the surface. (a) What is the discontinuity of the E-field at the surface of the shell. (b) What is the discontinuity of the E-field at the surface of the solid sphere? Also, find the magnitude and direction of the total electric field at: (c) r = 4 cm, (d) r = 8 cm, and (e) r = 13 cm.

x 30º

y

7) Use the same set-up in #6 with the following exceptions:

The solid sphere has a total charge of 5 μC and the shell has uniform surface charge density of 60 μC/m2. Answer the same questions in #6, (a) – (e).

8) You have a thin infinite

cylindrical shell of radius 8 cm and a uniform surface charge density of – 12 μC/m2. Inside the shell is an infinite wire with a linear charge density of 15 μC/m. The wire is running along the central axis of the cylinder. (a) What is the discontinuity of the E-field at the surface of the shell? Also, find the magnitude and direction of the total electric field at: (b) r = 4 cm, and (c) r = 13 cm.

9) You have a thin infinite

cylindrical shell of radius 15 cm and a uniform surface charge density of 10 μC/m2. Inside the shell is an infinite solid cylinder of radius 5 cm with a volume charge density of 95 μC/m3. The solid cylinder is running along the central axis of the cylindrical shell. (a) What is the discontinuity of the E-field at the surface of the shell? (b) What is the discontinuity of the E-field at the surface of the solid cylinder. Also, find the magnitude and direction of the total electric field at: (c) r = 4 cm, (d) r = 11 cm, and (e) r = 20 cm.

 

–

–

G L

+

 

 

10) You have a thick spherical shell of outer diameter 20 cm and inner diameter 12 cm. The shell has a total charge of – 28 μC spread uniformly throughout the object. Find the magnitude and direction of the total electric field at: (a) r = 6 cm, (b) r = 15 cm, and (c) r = 24 cm.

11) You have a thick cylindrical shell

of outer diameter 20 cm and inner diameter 12 cm. The shell has a uniform volume charge density of 180 μC/m3. Find the magnitude and direction of the total electric field at: (a) r = 6 cm, (b) r = 15 cm, and (c) r = 24 cm.

12)

You have an thin infinite sheet of charge with surface charge density of 8 μC/m2. Parallel to this you have a slab of charge that is 3 cm thick and has a volume charge density of – 40 μC/m3. Find that magnitude and direction of the total electric field at: (a) point A which is 2.5 cm to the left of the sheet, (b) point B which is 4.5 cm to the right of the sheet, and (c) point C which is 1 cm to the left of the right edge of the slab.

13)

You have an infinite slab of charge that is 5 cm thick and has a volume charge density of 700 μC/m3. 10 cm to the right of this is a point charge of – 6 μC. Find that magnitude and direction of the total electric field at: (a) point A which is 2.5 cm to the left of the right edge of the slab, (b) point B which is 6 cm to the right of the slab, and (c) point C which is 4 cm to the right of the point charge.

 

14) You have two infinite sheets of charge with equal surface charge magnitudes of 11 μC/m2 but opposite signs. Find the magnitude and direction of the total electric field, (a) to the right of the sheets, (b) in between the sheets, and (c) to the left of the sheets.

15)

A hydrogen molecule (diatomic hydrogen) can be modeled incredibly accurately by placing two protons (each with charge +e) inside a spherical volume charge density which represents the “electron cloud” around the nuclei. Assume the “cloud” has a radius, R, and a net charge of –2e (one electron from each hydrogen atom) and is uniformly spread throughout the volume. Assume that the two protons are equidistant from the center of the sphere a distance, d. Calculate, d, so that the protons each have a net force of zero. The result is darn close to the real thing. [This is actually a lot easier than you think. Start with a Free-Body Diagram on one proton and then do F = ma.]

 

ANSWERS:

 

 

NOTE: Units for 1 – 4

are CmN 2 1) a) 0 for F/B,  0.375 for L/R,  0.65 for T/B

b) & c) 0 2) a) – 1.81 x 10–8

b) – 9.05 x 10–9 3) 7.54 x 104 4) 5.66 x 104 5) a) 9.99 x 106 N/C, OUTWARD [O] b) 7.99 x 105 N/C

INWARD [I] 6) a) 6.29 x 106 N/C

b) 0 c) 9.04 x 106 N/C, I d) 7.63 x 106 N/C, I e) 8.36 x 105 N/C, O 7) a) 6.78 x 106 N/C

b) 0 c) 4.99 x 105 N/C, O d) 7.03 x 106 N/C, O e) 6.67 x 106 N/C, O

8) a) 1.36 x 106 N/C b) 6.74 x 106 N/C, O c) 1.24 x 106 N/C, O 9) a) 1.13 x 106 N/C b) 0 c) 2.15 x 105 N/C, O d) 1.22 x 105 N/C, O e) 9.15 x 105 N/C, O 10) a) 0 b) 2.94 x 106 N/C, I c) 4.37 x 106 N/C, I 11) a) 0 b) 5.49 x 105 N/C, O c) 1.09 x 106 N/C, O 12) a) 3.84 x 105 N/C, L b) 5.20 x 105 N/C, R c) 4.30 x 105 N/C, R 13) a) 3.84 x 105 N/C, R b) 3.57 x 107 N/C, R c) 3.18 x 105 N/C, L 14) a) 0 b) 1.24 x 106 N/C, R c) 0 15) 0.794R

10 cm

A B C

10 cm

A B –

C

R

+ +

d d

 

 

Physics 226 Fall 2013

 

Problem Set #6

NOTE: Any answers of zero must have some kind of justification. 1) You have a cylindrical metal shell of

inner radius 6 cm and outer radius 9 cm. The shell has no net charge. Inside the shell is a line of charge of linear density of – 7 μC/m. Find the magnitude and direction of the electric field at (a) r = 3 cm, (b) r = 7 cm, and (c) r = 13 cm. Also, calculate the surface charge density of the shell on (d) the inner surface and (e) the outer surface.

2) You have a uniformly charged

sphere of radius 5 cm and volume charge density of – 7 mC/m3. It is surrounded by a metal spherical shell with inner radius of 10 cm and outer radius of 15 cm. The shell has a net charge 8 μC. (a) Calculate the total charge on the sphere. Find the magnitude and direction of the electric field at (b) r = 13 cm and (c) r = 18 cm. Also, calculate the surface charge density of the shell on (d) the inner surface and (e) the outer surface.

 

3) Two 2 cm thick infinite slabs of metal are positioned as

shown in the diagram. Slab B has no net charge but Slab A has an excess charge of 5 μC for each square meter. The infinite plane at the origin has a surface charge density of – 8 μC/m2. Find the magnitude and direction of the electric field at (a) x = 2 cm, and (b) x = 4 cm. Also, calculate the surface charge density on (c) the left edge of A, (d) the right edge of A, and (e) the left edge of B.

4) A positive charge of 16 nC is nailed down with a #6 brad.

Point M is located 7 mm away from the charge and point G is 18 mm away. (a) Calculate the electric potential at Point M. (b) If you put a proton at point M, what electric potential energy does it have? (c) You release the

proton from rest and it moves to Point G. Through what potential difference does it move? (d) Determine the velocity of the proton at point G.

5)

All the charges above are multiples of “q” where

q = 1μC. The horizontal and vertical distances between the charges are 25 cm. Find the magnitude of the net electric potential at point P.

6) Use the same charge distribution as in problem #5 but

change all odd-multiple charges to the opposite sign. Find the magnitude of the net electric potential at point P.

7) A parallel plate setup has a distance

between the plates of 5 cm. An electron is place very near the negative plate and released from rest. By the time it reaches the positive plate it has a velocity of 8 x 106 m/s. (a) As the electron moves between the plates what is the net work done on the charge? (b) What is the potential difference that the electron moves through? (c) What is the magnitude and direction of the electric field in between the plates?

 

3 cm 5 cm 8 cm 0 10 cm

A B

– 8q

– 4q

+9q

+9q

– 5q

+6q +6q

+2q

P

+ M

G

–

 

 

 

8)

A uniform line of charge with density, λ, and length, L is positioned so that its left end is at the origin. See diagram above. (a) Determine an equation (using integration) for the magnitude of the total electric potential at point P a distance, d, away from the origin. (b) Calculate the magnitude of the electric potential at P if d = 2 m, L = 1 m, and λ = – 5 μC/m. c) Using the equation you derived in part a), calculate the equation for the electric field at point P. It should agree with the result we got in Lecture Example #19.

 

9) You have a thin spherical shell

of radius 10 cm with a uni- form surface charge density of 11 μC/m2. Centered inside the sphere is a point charge of – 4 μC. Using integration, find the magnitude of the total electric potential at: (a) r = 16 cm and (b) r = 7 cm.

10) You have a uniformly

charged sphere of radius 5 cm and volume charge density of 6 mC/m3. It is surrounded by a metal spherical shell with inner radius of 10 cm and outer radius of 15 cm. The shell has no net charge. Find the magnitude of the electric potential at (a) r = 20 cm, (b) r = 12 cm, and (c) r = 8 cm.

11) Use the same physical situation with the exception

of changing the inner sphere to a solid metal with a surface charge density of 9 μC/m2 and giving the shell a net charge of – 3 μC. Find magnitude of the electric potential at (a) r = 20 cm, (b) r = 12 cm, (c) r = 8 cm, and (d) r = 2 cm.

12) CSUF Staff Physicist & Sauvé Dude, Steve

Mahrley, designs a lab experiment that consists of a vertical rod with a fixed bead of charge Q = 1.25 x 10–6 C at the bottom. See diagram. Another bead that is free to slide on the rod without friction has a mass of 25 g and charge, q. Steve releases the movable bead from rest 95 cm above the fixed bead and it gets no closer than 12 cm to the fixed bead. (a) Calculate the charge, q, on the movable bead. Steve then pushes the movable bead down to 8 cm above Q. He releases it from rest. (b) What is the maximum height that the bead reaches?

 

 

13)

d

P

0 – – – – –

+

L 20 cm

You have two metal spheres each of diameter 30 cm that are space 20 cm apart. One sphere has a net charge of 15 μC and the other – 15 μC. A proton is placed very close to the surface of the positive sphere and is release from rest. With what speed does it hit the other sphere?

14) A thin spherical shell of radius, R, is centered at the

origin. It has a surface charge density of 2.6 C/m2. A point in space is a distance, r, from the origin. The point in space has an electric potential of 200 V and an electric field strength of 150 V/m, both because of the sphere. (a) Explain why it is impossible for r < R. (b) Determine the radius, R, of the sphere.

– 4 μC 12 μC 15) – – +

6 cm The two charges above are fixed and cannot move. Find a

point in space where the total electric potential will equal zero.

 

 

ANSWERS:

1) a) 4.20 x 106 N/C, I

b) 0 c) 9.68 x 105 N/C, I d) 1.86 x 10–5 C/m2 e) – 1.24 x 10–5 C/m2 2) a) – 3.67 x 10–6 C b) 0 c) 1.20 x 106 N/C, O d) 2.92 x 10–5 C/m2 e) 1.73 x 10–6 C/m2 3) a) 7.35 x 105 N/C, L

b) 0 c) 6.5 x 10–6 C/m2 d) – 1.5 x 10–6 C/m2 e) 1.5 x 10–6 C/m2 f) – 1.5 x 10–6 C/m2 4) a) 2.06 x 104 V b) 3.29 x 10–15 J c) – 1.26 x 104 V d) 4.91 x 105 m/s 5) 5.02 x 105 V

6) – 7.87 x 104 V 7) a) 2.92 x 10-17 J b) 182.2 V c) 3644 N/C

8) a)   

   

d Ldlnk

b) – 1.83 x 104 V 9) a) – 1.47 x 105 V b) – 3.90 x 105 V 10) a) 1.41 x 105 V b) 1.88 x 105 V c) 2.59 x 105 V 11) a) – 8.37 x 104 V b) – 1.12 x 105 V c) – 8.62 x 104 V d) – 9900 V 12) a) 2.48 x 10–6 C b) 1.42 m 13) 1.4 x 107 m/s 14) 2.86 m 15) 1.5 cm

q

Q

 

 

Physics 226 Fall 2013

 

Problem Set #7 1) You have a parallel plate capacitor of plate separation

0.1 mm that is filled with a dielectric of neoprene rubber. The area of each plate is 1.8 cm2. (a) Calculate the capacitance of the capacitor. The capacitor is charged by taking electrons from one plate and depositing them on the other plate. You repeat this process until the potential difference between the plates is 350 V. (b) How many electrons have been transferred in order to accomplish this?

2) A capacitor with ruby mica has an effective electric field

between the plates of 4600 V/m. The plates of the capacitor are separated by a distance of 4 mm. 50 mJ of energy is stored in the electric field. (a) What is the capacitance of the capacitor? (b) Calculate the energy density in between the plates.

3) A capacitor with a dielectric of paper is charged to 0.5 mC.

The plates of the capacitor are separated by a distance of 8 mm. 40 mJ of energy is stored in the electric field. (a) What is the strength of the effective electric field? (b) Calculate the energy density in between the plates.

4) A capacitor of 10 μF is charged by connecting it to a

battery of 20 V. The battery is removed and you pull the plates apart so that you triple the distance between them. How much work do you do to pull the plates apart?

5) The flash on a disposable camera contains a capacitor

of 65 F. The capacitor has a charge of 0.6 m C stored on it. (a) Determine the energy that is used to produce a flash of light. (b) Assuming that the flash lasts for 6 ms, find the power of the flash. (Think back to 225.)

6) A spherical shell conductor of

radius B encloses another spherical shell conductor of radius A. They are charged with opposites signs but same magnitude, q. (a) Using integration, derive an equation for the capacitance of this spherical capacitor. (b) Calculate the capacitance if A = 45 mm and B = 50 mm. (c) If q = 40 μC, what is the energy density in between the shells?

 

7) You attach a battery of 15 V to an air-filled capacitor of 5 μF and let it charge up. (a) If the plate separation is 3 mm, what is the energy density in between the plates? You then remove the battery and attach the capacitor to a different uncharged capacitor of 2 μF. (b) What is the amount of charge on each capacitor after they come to equilibrium?

8) You attach a 100 pF capacitor to a battery of 10 V. You

attach a 250 pF battery to 7 V. You remove both of the batteries and attach the positive plate of one capacitor to the positive plate of the other. After they come to equilibrium, find the potential difference across each capacitor.

9) Do problem #8 but when you attach the capacitors

together attach the opposite sign plates instead of the same sign plates.

10)

Determine the equivalent capacitance between points A and B for the capacitors shown in the circuit above.

11)

Determine the equivalent capacitance between points A and B for the capacitors shown in the circuit above.

12) Design a circuit that has an equivalent capacitance of

1.50 μF using at least one of each of the follow capacitors: a 1 μF, a 2 μF, and a 6 μF. [You must also show where your A and B terminals are located.]

 

A

20 F

4 F

4 F

6 F

12 F

B

30 F

A 12 F

18 F 6 F

20 F

B

12 F 75 F

 

 

13) The two capacitors above both have plates that are

squares of sides 3 cm. The plate separation is 1.2 cm for both. Between each of the capacitor plates are two different dielectrics of neoprene rubber and Bakelite. Everything is drawn to scale. Find the capacitance of each capacitor. (HINT: Think series and parallel.)

14) The plates of an air-filled capacitor have area, A, and are

separated by a distance, d. The capacitor is charged by a battery of voltage, V. Three things are going to change: (1) The plates of the capacitor are pulled apart so that the distance between the plates triples. (2) The area of the plates increase by a factor of 6. (3) The voltage of the battery decreases by a factor of 4. Determine expressions in terms of A, d, and/or V for (a) the new capacitance, (b) the new charge, and (c) the new energy density.

 

15)

A massless bar of length, L, is hanging from a string that is attached 1/3 of the length of the bar from the right end. A block of mass, M, is hung from the right end. The left end of the bar has an air-filled massless capacitor of plate area, A, and plate separation, d. Find an expression for the potential difference between the plates so that this system is in equilibrium. (HINT: You will

need the equation dx dU

F  from 225.)

 

ANSWERS:

(a) (b)

1) a) 1.067 x 10–10 F

b) 2.34 x 1011 e–

2) a) 2.95 x 10–4 F b) 5.05 x 10–4 J/m3 3) a) 2 x 104 V/m

b) 6.7 x 10–3 J/m3 4) 4 x 10–3 J 5) a) 2.8 x 10–3 J b) 0.467 W

6) a)

AB AB4C o

b) 5.01 x 10–11 F c) 1.125 x 105 J/m3 7) a) 1.11 x 10–4 J/m3 b) 2.14 x 10–5 C, 5.36 x 10–5 C

8) 7.86 V 9) 2.14 V 10) 4 μF 11) 9 μF 13) a) 3.85 pF b) 3.76 pF

14) a) d

A2 C o

 

b) d2 AV

Q  o

c) 2 2

o

d288 Vu

15) A

Mg dV

o

M

 

 

Physics 226 Fall 2013

 

Problem Set #8 1) Analyze the circuit below using a QCV chart. You must

show appropriate work for full credit. 2) Analyze the circuit below using a QCV chart. You must

show appropriate work for full credit. 3) Analyze the circuit below using a QCV chart. You must

show appropriate work for full credit. 4)

An Oppo Digital Blu-Ray player [DMP-95] (Yes, I am an audiophile.) has a power cable which has a metal that allows 9 x 1019 electrons per cubic millimeter. On average, the cable passes 1 x 1022 electrons every hour. The electrons passing through the player have a drift velocity of 4.5 μm/s. (a) What current does the Oppo draw? (b) Calculate the diameter of the cable?

5) The Large Hadron Collider at CERN creates proton beams which collide together resulting in pictures like the one at the right. Some of these beams can have a radius of 1.1 mm with a current of 1.5 mA. The kinetic energy of each proton in this beam is 2.5 MeV. (a) Calculate the number density of the protons in the beam. (b) If the beam is aimed at a metal target, how many protons would strike the screen in 1 minute?

C1 = 8 μF C2 = 15 μF

20 V

C3 = 30 μF

6)

Two copper wires are soldered together. Wire #1 has a radius of 0.7 mm. Wire #2 has a radius of 1.2 mm. Copper has a number density of 8.47 x 1028 e–/m3. The drift velocity in Wire #1 is 0.72 mm/s. If you want the current to remain the same in both, what is the drift velocity in Wire #2?

7) A nichrome cable has a current of 140 A running through

it. Between two points on the cable that are 0.22 m apart, there is a potential difference of 0.036 V (a) Calculate the diameter of the cable. (b) How much heat energy does this part of the wire emit in 1 minute?

8) A “Rockstar” toaster uses a

tungsten heating element (wire). The wire has a diameter of 1.2 mm. When the toaster is turned on at 20 C, the initial current is 1.6 A. (a) What is the current density in the wire? (b) A few seconds later, the toaster heats up and the current is 1.20 A. What is the temperature of the wire? (c) If the toaster is plugged into a standard wall outlet in Kankakee, Illinois, what is the rate that energy is dissipated from the heating element?

9) Skid runs a 10 mile line of copper cable out to his shack in

the sticks so he can have electricity to play Lord of the Rings Online. At 20ºC the resistance of the cable is 12 . At 50ºC the cable emits 1.5 kJ every second. (a) What is the resistance of the cable at 50ºC? (b) What is the current running through the cable at 50ºC? (c) Calculate the current density at 50ºC.

 

C1 = 18 F

Wire #1 Wire #2 C2 = 6 μF

C3 = 4 μF

C4 = 30 μF 25 V

C1 = 5 F C2 = 4 μF

15 V C3 = 1 μF

C4 = 12 μF

 

 

10) A modern hair dryer uses a nichrome heating element that typically is 30-gauge wire around 40 cm in length. The gauge rating on a wire refers to its diameter. In this case, 30-gauge wire has a diameter of 0.254 mm. Nichrome has a number density of 7.94 x 1028 e–/m3. If the drift velocity of the electrons in the wire is 18.7 mm/s, what is the voltage that the hair dryer is plugged into?

 

11) Before LCD, LED, Plasma,

and (the latest) OLED TVs, there were CRT (Cathod-Ray Tube) TVs. Inside these TVs were electron guns that shot an electron beam of diameter 0.5 mm and current density of 244 A/m2 onto the inside of a glass screen which was coated with phosphor. How many electrons would hit the phosphor every minute?

12)

Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.

 

13)

Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.

14)

Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.

15) Design a circuit that has an equivalent resistance of

1.00  using at least one of each of the follow resistors: a 1 , a 2 , and a 6 . [You must also show where your A and B terminals are located.]

 

ANSWERS:

NOTE: Some of these answers are minimal since there are checks that you can do to verify your answers.

 

A

27 

B 54 

8 

30 

16 

14 

10 

30 

B

18 

96 

6 

32  18 

60  A

A

20 

30 

B

30 

7 

50 

12 

45 

60 

1) CEQ = 18 μF 8) a) 1.415 x 106 A/m2 2) CEQ = 6 μF b) 94.1ºC 3) CEQ = 2 μF c) 144 W

9) a) 13.4  4) a) 0.444 A b) 2.96 mm b) 10.58 A

c) 5.14 x 105 A/m2 5) a) 1.13 x 1014 p+/m3 b) 5.63 x 1017 p+ 10) 95.0 V 6) 0.262 mm/s 11) 1.8 x 1016 e–

7) a) 0.033 m 12) 4  b) 302 J 13) 14  14) 22 

 

 

Physics 226 Fall 2013

 

Problem Set #9

NOTE: You can only use circuit tricks on 9 – 11 but not on any others. 1) Analyze the following circuit using a VIR chart. 2) Swap the location of the battery and R1 in the circuit from

problem #1. Analyze the circuit using a VIR chart. 3) Analyze the following circuit using a VIR chart. 4) The battery in this problem has an internal resistance of

0.15 . (a) Analyze the following circuit using a VIR chart. (b) Is this circuit well designed? Discuss, explain.

 

5) Analyze the following circuit using a VIR chart.

6) Analyze the following circuit using a VIR chart. 7) The battery in this problem has an internal resistance of

1 . (a) Analyze the following circuit using a VIR chart. (b) Is this circuit well designed? Discuss, explain.

8) A load of 3.5  is connected across a 12 V battery. You

measure a voltage of 9.5 V across the terminals of the battery. (a) Find the internal resistance of the battery. (b) Is this circuit well designed? Discuss, explain.

9) Analyze the circuit from problem

#5 using a VIR chart. You are using only the diagram in #5, not the values. New values are given at the right. You may use a circuit trick for this circuit, but only for ONE value.

10) Analyze the circuit from problem

#6 using a VIR chart. You are using only the diagram in #6, not the values. New values are given at the right. You may use a circuit trick for this circuit, but only for ONE value.

 

R1

20 V

R2 R3 R4

R5

Given: R1 = 12  R2 = 3  R3 = 8  R4 = 36  R5 = 15 

 

50 V

R1 Given: R1 = 28  R2 = 6  R3 = 84  R4 = 7  R5 = 54 

 

R3

R2

R4

R5

55 V

R1 Given: R1 = 18  R2 = 32  R3 = 15  R4 = 21  R5 = 42  R6 = 30  R7 = 52 

R3

R2

R4 R5

R6 R7

R1

VB

R2

R3 R4

Given: VB = 60 V V2 = 50 V

 

I1 = 2 A I4 = 3 A

 

R3 = 8 

R1

VB

R2 R3

R4

R5

Given: V5 = 32 V

 

I2 = 0.4 A I4 = 0.5 A

 

R1 = 36  R6 R3 = 60  R4 = 36  R6 = 32 

R1

VB

Given: VB = 32 V

 

R2 I1 = 4 A R3 R3 = 12 

R4 R4 = 8 

Given: VB = 63 V R1 = 8  R2 = 20  R3 = 35  R4 = 49 

 

Given: VB = 75 V R1 = 16  R2 = 40  R3 = 48  R4 = 24  R5 = 8  R6 = 24 

 

 

11) Analyze the following circuit using a VIR chart. 12) Using the information you are

given for the circuit at the right, answer the following. (a) Determine the magnitude and direction of the current in the circuit. (b) Determine which point, A or B, is at a higher potential.

13) Calculate the unknown currents I1, I2, and I3 for the circuit

below.

14) Calculate the unknown currents I1, I2, and I3 for the circuit below.

Given: 15) Calculate the unknown currents I1, I2, and I3 for the circuit

below.

ANSWERS:

NOTE: These answers are minimal since there are checks that you can do to verify your answers.

 

R1 R2

R3 R4

R5 R6

I1 8 V VB = 50 V

R1 = 9  R2 = 4  R3 = 18  R4 = 4  R5 = 7  R6 = 12 

B

A

17 V

13  7 

5 

11 

23 V

6 

1 

10 V

25 V

3 

5 

7 

I1

I2

I3

4 

9 

10 

4  7 

I2

6 

I3 22 V

3  10 V I1

4 

4  25 V

2  5 

I2 I3

20 V 4 

7) REQ = 8  1) REQ = 2  8) a) 0.923  2) REQ = 11.48  9) REQ = 21  3) REQ = 25  10) REQ = 25  4) REQ = 12.15  11) REQ = 20  5) REQ = 12  12) a) 1.11 A 6) REQ = 40 

 
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Physic II Experiment: AC Circuits

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While completing the experiment AC Circuits, make sure to keep the following guiding questions in mind :

•What is the relationship between the energy stored in the inductor and the energy stored in the capacitor when a power source is not present in the circuit? .

•How is energy dissipated in an AC circuit, within a resistor, within a capacitor, and within an inductor? .

•What are some of the applications of resonance in electrical and mechanical engineering? Is resonance always desirable? .

 

To complete the experiment you will need to:

1.Be prepared with a laboratory notebook to record your observations. .

2.Click the image to open the simulation experiment. .

3.Perform the experiment as described. .

4.Transfer your data and results from your laboratory notebook into the lab report template provided at the end of this experiment description. .

5.Submit your version of the laboratory experiment report. .

 

In your laboratory notebook, you will collect data, make observations, and ponder the questions posed within the lab instructions. Thus, the notebook should contain all the data collected and analysis performed, which will be invaluable to you as you write the results section of your laboratory report. Furthermore, the notebook should contain your observations and thoughts, which will allow you to address the questions posed, both for the discussion section in the laboratory report and in helping you to participate in the online discussion included in the module.

 

 

 

 

 

Part I –LC Circuit

· Start the simulation “Circuit Construction Kit (AC +DC)” (if you haven’t done so already) by clicking on the image below.

http://phet.colorado.edu/sims/circuit-construction-kit/circuit-construction-kit-ac_en.jnlp

· Build a circuit that has a battery, a capacitor and a switch.

· Right click on the capacitor and choose “change capacitance.” Use the slider to vary the capacitance.

http://phet.colorado.edu/sims/circuit-construction-kit/circuit-construction-kit-ac_en.jnlp

 

What behavior in the circuit do you observe when you close the switch? Do you observe any changes in the indications of charge stored on the plates of the capacitor? As the capacitance increases, what changes do you observe in the current and charge stored on the capacitor plates?

· Set the capacitor at 0.09 Farad. Carefully disconnect the battery from the circuit and build a new circuit with the charged capacitor (still at 0.09 Farad) and an inductor set at 11 Henrys—no battery.

· Bring the Current Chart to your circuit, and place the detector over a wire. You may have to adjust the +/- buttons for a good reading. Recall that the time for one cycle is called the period, and the frequency is equal to 1/period. In your laboratory notebook, record the values for capacitance, inductance, period, and frequency.

Use the definition of the resonant frequency from the module notes to calculate the resonate frequency of the AC circuit. How does this compare to the measured operating frequency of the LC circuit? Repeat this procedure for two other values of inductance and capacitance. Record the results in your laboratory notebook.

Part II – Phase Shift in an AC Circuit

· Build a circuit that has a capacitor and an AC source.

· Bring the Current Chart to your circuit, and place the detector over a wire. You may have to adjust the +/- buttons for a good reading.

· Bring the Voltage Chart to your circuit, and place the probes over the terminals of the capacitor. You may have to adjust the +/- buttons for a good reading.

Use the time scale on the horizontal scale of the Voltage Chart to measure the period of the voltage signal. Is the period for the potential the same as that measured for the current? Are the graphs on the two charts in phase? In other words do the peaks on the Current Chart and the Voltage Chart occur at the same time, or are they offset by some interval of time? Determine the value of this phase shift and whether current leads or trails voltage. (Note: If the period to complete 1 full cycle represents 360 degrees or 2π radians, then an offset between the peaks of ¼ of the full period represents 90 degrees or π/4 radians.)

· Replace the capacitor with an inductor. Determine the value of this phase shift, if any, and whether current leads or trails voltage. What is the relationship of this phase shift, if any, to that of the capacitor?

Part III – Resonance

An LC circuit initially charged will oscillate with energy flowing back and forth between the inductor and the capacitor. A circuit like this loses very little energy because neither inductors nor capacitors dissipate energy in the same manner as a resistor. If this circuit is driven by an external source at its natural frequency, energy will be added to the system during each cycle. In other words, the circuit will resonate, and exhibit oscillations with large currents.

· Construct an AC circuit with a capacitor, and inductor, and an AC current source.

· Set the capacitance to C = 0.09 Farad and the inductance to L = 11 Henrys.

· Right click the power source and set its frequency to a value that is not the resonant frequency of the circuit. Wait at least 2 minutes, and then write down your observations in your laboratory notebook.

· Pause the simulation, and reset the AC frequency so that it is equal to the resonant frequency of the circuit. Wait at least 2 minutes, and then describe your observations in your laboratory notebook. Be sure to point out any similarities or differences with the previous step.

· Add a resistor to the circuit with a very small resistance, R =0.01Ohms. Measure the peak current at frequencies (ƒ) equal to multiples of the resonance frequency. In particular, try frequencies equal to 0.5, 0.75, 0.9., 1.0, 1.1, 1.25, and 1.5 times the resonance frequency (ƒο).

Use your favorite spreadsheet program to plot peak current as a function of frequency on a scatter plot. Do not insert a trendline.

 
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Lab Report Help

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Lab Exercise 5: Centripetal Acceleration

  • Follow the instructions and directions below for this lab.  Disregard the outline in the manual for your LabPaq Kit.
  • Read this document entirely before starting your work.
  • Do not forget to record your measurements and partial results.
  • Submit a Laboratory Report through Moodle, as shown in the last section of this outline.  Remember that the Laboratory Report should include the answers to the questions below.

GOALS

(1) To calculate the angular velocity of a spinning object using varying hanging and rotational masses and varying radii

(2) To calculate the theoretical centripetal force;

(3) To calculate the experimental centripetal force.

INTRODUCTION

When objects, such as a carousel, move in a uniform circular motion, they are moving at a constant speed, while their direction of velocity is changing. The word centripetal means center seeking. When acceleration of a circular moving object is directed toward the center, the acceleration is centripetal and the acceleration is called centripetal acceleration.

Newton’s first and second laws of motion state that an object moves at a constant speed in a straight line unless an external force acts upon that object and that a force causes an object’s acceleration. By following theses laws, the force on a circular moving object is called centripetal force. Centripetal force accelerates an object by changing the direction of its velocity without changing its speed.

Mathematically, centripetal acceleration is represented as:

PHY-115_Lab-5_introduction.PNG

with ac being the centripetal acceleration, v the velocity and r the radius of the circle.

The centripetal force, in turn, can be represented as:

 PHY-115_Lab-5_introduction-2.PNG

with Fc being the centripetal force and m the mass of the object.

An example of centripetal acceleration is the Earth/Moon relationship. Earth and the Moon exert gravitational forces on each other and the Moon undergoes centripetal acceleration toward the center of Earth.

PROCEDURE

In this experiment, a rubber stopper is connected to a string and is rotated in a horizontal circle. The tension in the string causes the stopper to undergo centripetal acceleration.

Rotational Velocity

The period of revolution or period—the time it takes for the object to complete one revolution— is represented by T (this is similar to the notation we used in the previous laboratory with the pendulum apparatus). The speed v of the rotating object is calculated by dividing the circumference of the circle of radius r (2πr) by T. This velocity can be referred to as rotational velocity or angular velocity.

PHY-115_Lab-5_equation 3.PNG

Therefore, to determine the constant velocity of a rotating object, we need to measure the time T required to make one revolution using the following equations:

 PHY-115_Lab-5.PNG

In addition to centripetal acceleration, the force of gravity acts on the rubber stopper as it is whirled along a horizontal plane. Because gravity acts perpendicular to the centripetal force, the orbital plane of the rotating mass lies below the horizontal plane at the top end of the vertical tube. Despite these factors, the data obtained from this experiment should be reasonable approximations that demonstrate the basic relationships among the variables.

 Constant mass, variable radius.

In this section we will investigate the effects of changing the radius of the system on the centripetal force.

Choose an area that is free from obstructions and breakable objects. You will be swinging weights on a string and if these weights break free, they could potentially hit objects or people. Choose an area where only your assistant is present to reduce the risk of people being injured.

 Wear goggles so that the rotating stopper does not hit your eyes.

Record the number of washers from your kit in Table 1. Place all of the washers into a bag to weigh their mass and record the total mass in Table 1. Find the average mass of each washer in kilograms and record it in Table 1.  Also weigh the mass of the rubber stopper.

 

Pull out the 4.0 m of string provided in your apparatus kit.

Tie a the 4m string to a rubber stopper (the rotating mass), slide the string through a glass cylinder, and tie the string to our hanging mass. Before threading the string through the glass rod, make sure the smooth end of the glass rod is at the top nearest the rotating rubber stopper.

Thread about 30 g of washers onto the end of the string opposite from the stopper. Record this constant hanging mass.  User paper clips to ensure that the washers do not fly away.  If needed, open up the paper clip to secure the washers. Figure 3 shows a detail of this.

QUESTION 1

What is the actual (measured) mass of the washers?

 Figures 1, 2 and 3 show the experimental setup.

 

Figure 1: Experimental setup

Figure 2: Another picture of the experimental setup.

 

Figure 3: Details of Washers at one end.

 Tie another paper clip about 20 cm above the washers. When finished, your apparatus should look like the one in Figure 4.

 

Figure 4: Experimental setup

 Pull the string through the glass rod so that approximately 0.7 m of string is between the glass rod and stopper. Practice swinging the stopper around in a circle over your head as shown in Figure 5 while holding onto the glass rod. Support the suspended mass containing the washers with one hand and hold the rod in the other. Be careful and review the safety precautions at the beginning of this procedure.

 Figure 5:  Student working in the experiment (Picture courtesy of Chad Saunders, TESU student)

Swing the stopper in a circular motion. Slowly release the hanging mass and adjust the rotating speed of the stopper so that the paper clip attached to the string above the washers stays a few centimeters below the bottom of the tube, neither rising nor falling.

Do not move your hand too much while swinging the stopper. Ideally, the steel washers should be stationary. Keeping your hand steady will help the rubber stopper move smoothly. Practice stopping the spin while simultaneously grasping the string just above the tube. This action will allow you to measure the radius of the spin circle, which is the length of the string from the top of the tube to the center of the stopper.

Stop spinning the rubber stopper and use the measuring tape to measure the length of the string in meters. This is the length of the string between the glass tube and rubber stopper.

Record this length as the radius for Radius 1 in Table 2.

Once you are able to spin the stopper with a steady pace, you can begin the experimental portion of the lab.

As you continue with the experiment, complete the appropriate cells in Table 2.  Note the following:

  • To estimate the time for 1 revolution, divide the time for 10 revolutions by 10.
  • Use the radius in each row to calculate the length of the circumference.
  • The velocity can be estimated dividing the length of the circumference by the time necessary for 1 revolution
  • The last column (velocity2) is calculated by squaring the previous column.

 

Begin to spin the apparatus, maintaining a constant radius. After the spin is stabilized, have an assistant use a stopwatch to time (in seconds) 10 revolutions. Record this 10-rev time for Radius 1 in Table 2.

Shorten the length of string between the stopper and the top of the glass tube by approximately 10 cm. Pull the string through the bottom of the glass tube to shorten the distance L between the top of the glass tube and the stopper. Use the tape measure to record this new length between the top of the glass rod and the stopper as the radius for Radius 2 in Table 2.

Repeat the procedure of swinging the stopper for 10 revolutions while it is being timed. Record the time for 10 rev in Table 2 for Radius 2.

Shorten the string by another 10 cm as done before and record this new radius in Table 2 for Radius 3.

Repeat the procedure of swinging the stopper for 10 revolutions while it is being timed. Record the time for 10 rev in Table 2 for Radius  3.

Once again, shorten the string by another 10 cm. Record this new radius in Table 2 for Radius 4.

Repeat the procedure of swinging the stopper for 10 revolutions while it is being timed. Record the time in Table 2 for Radius 4.

 Constant radius, variable hanging mass

Adjust the radius of the rotating mass to 0.5 m. Because this value will remain the same for this part of the experiment, we can record the length of the radius in Table 3 for all experiments in this section.

Change the number of hanging washers so that they weigh approximately 30 g. Record this hanging mass in Table 3 for Mass 1.

Use this 30-g hanging mass to perform one trial of 10 rev in a manner similar to that in Section 3.1  Record the time in Table 3 for Mass 1.

Complete the other columns for Mass 1.

Add more washers until the hanging mass is approximately equal to 40 g.  Repeat the process and complete the appropriate columns, now for Mass 2.

Repeat the experiment for a mass of 50 g  (Mass 3) and a mass for 60 g (Mass 4) as the mass of the hanging washers.

 

 Constant radius, variable rotating mass

Adjust the radius of the rotating mass to 0.5 m. Because this value will remain the same for this part of the experiment, we can record the length of the radius in Table 3 for all experiments in this section.  Adjust the mass of the hanging washers to 50 grams.

We will increase the mass of the stopper by adding two washers each time.  To do this, untie the knot and tie two washers with the stopper. You can estimate the new rotating mass by using your data from Table 1.  If you cannot untie the knot, cut it and readjust the string to a length of 50 cm.

Repeat the previous processes and record your data and calculations for Mass 1.

Add two more washers to the stopper (total of 4 washers) and complete the data for Mass 2.

Add an additional two washers and complete the data for Mass 3.

Add two more washers and complete the data for Mass 4.

 

 

DATA CALCULATIONS

The theoretical centripetal force (FC) is given by:

PHY-115_Lab-5-equation-section 4.JPG

 Note that the hanging mass must be in kg and the resulting force will be in N.

The experimental centripetal force (FC) is given by

PHY-115_Lab-5-equation2-section 4.JPG

Complete Tables 5, 6 and 7 in which we compare the theoretical centripetal force with the measured centripetal force.

 

QUESTION 2

What is the relationship between the radius and the velocity of a rotating object?

 

QUESTION 3

What is the relationship between the velocity of rotating object and the centripetal force exerted on it?

 

QUESTION 4

What is the relationship between the mass of a rotating object and its velocity?

 LABORATORY REPORT

Create a laboratory report  using Word or another word processing software  that contains at least these elements:

 Introduction:  what is the purpose of this laboratory experiment?

  • Description of how you performed the different parts of this exercise.  At the very least, this part should contain the answers to questions 1-4 above.  You should also include procedures, etc.   Adding pictures to your lab report showing your work as needed always increases the value of the report.
  • Conclusion: What area(s) you had difficulties with in the lab; what you learned in this experiment; how it applies to your coursework and any other comments.
 
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Physic Lab

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Balancing Act Homework Activity 1

Name__________________________________

Learning Goals: Students will be able to determine the variables that affect the balancing of

a seesaw and predict where an object of a certain mass will have to be placed to balance the

seesaw.

Directions: Log in to http://www.colorado.edu/physics/phet and click on Physics in the left

hand column and then choose the Balancing Act icon. Choose “Run Now” to start the

simulation.

1. Investigate Balancing Act using the Intro tab at the top by moving the tanks and trash

cans around and removing the supports to try to balance the seesaw. While you play

with this tool, make observations about when the beam balances and when it doesn’t.

Use the tools on the side (mass labels, rulers, forces from objects and the level) to

help you make your observations. Describe what you discovered about balancing the

seesaw.

! !

2. Use the scenarios below to make predictions about where the 10kg trash can would

need to be placed, without using Balancing Act. Sketch what you think the beams

would look like for the following scenarios and justify your reasoning.

Scenario 1:

!

Justification:

Scenario 2:

!

Justification:

! ! Scenario 3:

!

Justification:

3. Now, use the Balancing Act simulation to verify or correct your predicted scenarios and

justification with a different color pen.

Next, click on the Game tab in the upper left. Try several scenarios at the different levels for

a minute or two each.

4. What changes can you make to your reasoning about how to balance the beam to

reconcile your previous thinking with the things you have discovered?

! 5. Explain what factors affect the balancing of the beam and describe how each factor

appears to affect the balancing.

! ! !

6. Now suppose you go to the park with a younger, smaller child. How would you use this

information so the two of you could use the seesaw even though you are not the same

size?

! ! !

! ! ! Balancing Act Activity 2 Name

___________________________

Learning Goal: Students will calculate where a mass needs to be placed on a beam to

balance the beam and then confirm or correct their calculations using the Balancing Act

simulation.

Investigation:

1. Calculate where the 80 kg man would need to sit to balance the beam. Show all work

including formulas and substitutions with units.

! !!

Click on the Balance Lab tab on the upper left of the simulation and test your calculations.

You may need to use the yellow arrows in the brick box to scroll to the man and child.

Evaluate your calculations. (How’d you do?)

! ! !

2. Predict where you would place the 20kg pile of bricks to balance the beam? Show all

calculations including formula and substitutions with units.

!

Now test your predictions and calculations using the Balance Lab tab. Evaluate your

calculations.

!! 3. Calculate where a 15kg pile of bricks would need to be placed to balance the beam.

Show all calculations.

!Evaluate your calculations using the simulation.

! ! ! ! Finally, using the Balancing Lab tab and scrolling to the mystery packages, determine

the mass of each package. Show all work including formulas and substitutions with

units.

! Package

! Calculation

Where did you place the package on the beam?

Where did you place the package on the beam?

 
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LAB PHYSICS Lab 7: Conservation Of Momentum

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PHYSICS 182A/195L LAB REPORT – LAB 7: CONSERVATION OF MOMENTUM

Lab 7: Conservation of Momentum San Diego State University Department of Physics Physics 182A/195L

TA:
Lab partner 1:
Lab partner 2:
Date:
Score:

 

Data has been entered in blue.

Theory

What is momentum? Momentum is the product of a body’s mass  and it’s velocity:

 .

Of the fundamental kinematic quantities, mass, position, velocity, acceleration, why does the product of mass and velocity deserve its own name? It turns out that mass times velocity, momentum, is what’s known as a conserved quantity.

Consider Newton’s third law  for the forces experienced by two interacting masses  and  . By replacing each force by  , we can show the following:

This equation says that the quantity in the parenthesis does not change with time. Another way to say this is that the term in parenthesis is a constant:

This fact is so important that we give  its own name and symbol,  :

This important result shows us that the total momentum of a system is constant. We say:

Momentum is always conserved.

Collisions

While a collision can be extremely complex and involve many forces and bodies (imagine a car crash), conservation of momentum tells us that the total momentum before and after that collision is the same:

The (i) subscript labels the initial momentum (before the collision) and the (f) subscript labels the final momentum (after the collision).

Elastic Versus Inelastic Collisions

Yet another quantity of interest is kinetic energy. Kinetic energy is defined as:

Kinetic energy is only sometimes conserved during a collision. If kinetic energy is conserved during a collision, then we call it an Elastic collision. This only happens for frictionless collisions. Otherwise, if the kinetic energy is not conserved, then we call it an Inelastic collision and kinetic energy is lost due to internal friction.

The Experiment!

In this lab, we will demonstrate that conservation of momentum works as we expect. Imagine we have two carts with masses  and  . Cart 1 is initially moving with some known velocity  , and Cart 2 is at rest  . We know both cart’s initial speeds and we want to determine the final speed of each cart, after the collision.

Elastic Collision

In an elastic collision, we can use the fact that both momentum is conserved and kinetic energy is conserved. We therefore have two equations:

 ,

and

 .

In our experiment, we assume that we know  and we know  . So our equations simplify:

 ,and .After a few lines of algebra, we can solve these two equations for both  and  , which are the final speeds of Cart 1 and Cart 2 after the collision, respectively. The details for solving these equations are shown in the Appendix. The final results are:

Let’s see what these equations predict for three different values of  and  :

 

Elastic predictions Description
Part A: Equal masses

[plug in m1=m2]

 Cart 1 comes to rest and Cart 2 has a final speed equal to the initial speed of Cart 1.
Part B: Cart 2 weighs twice as much.

[plug in 2m1=m2]

 Cart 1 bounces off of the heavier Cart 2, and Cart 2 moves off in the positive direction. Both carts are moving slower than Cart 1’s initial speed.
Part C: Cart 1 weighs twice as much.

[plug in m1=2m2]

 Both carts end up moving in the positive direction, with the heavier Cart 1 moving slower, and the lighter Cart 2 moving faster, than Cart 1’s initial speed.

Inelastic Collision

While an elastic collision maintains both the conservation of momentum and kinetic energy, an inelastic collision only conserves momentum. This creates a problem for our equations because we no longer have two sets of equations to work with.

There is one special case where we can still find  and  , and that’s when  . What would this mean? It implies that the two carts stick together after the collision. This results in a perfectly inelastic collision.

If  is known and  , conservation of momentum tells us

 ,like before. If we plug-in  , we get

 .Now we can easily solve for the unknown  :

 .Let’s see what these equations predict:

 

Inelastic predictions Description
Equal masses

[plug in m1=m2]

 Both carts move to the right with half of Cart 1’s initial speed.

Procedure

Setup

1. Make sure that both carts have magnetic bumpers on them.

2. Make sure the track is level. You can adjust screws on the track feet to change the incline. When you place a cart at rest on the track, give it a little push in each direction. It should not accelerate in either direction.

3. Use a scale to find the mass of each cart. If the carts do not have the same mass, add weights to one of them until they are the same mass.

4. Record the mass of each cart in their respective columns in Table 1.1 on the Data page.

Section 1: (Perfectly) Inelastic Collision

1. Place the red and blue carts at rest with the Velcro® bumpers facing each other. The blue cart should be in the center of the track and the red cart should be on the left end.

2. Start recording and give the red cart a push toward the blue cart. Stop recording before either cart reaches the end of the track.

3. On the velocity vs. time graph, find the velocity of the red cart just before and just after the collision. You can accomplish this using the coordinate tool. The time just before the collision is most easily identified by finding the time  when the blue cart first begins to move. Record these velocities in Table 1.2.

4. The initial velocity of the blue cart is zero and its final velocity is the same as the red cart because they stick together. Record the blue cart’s final velocity in Table 1.2.

5. Add together the sum of the initial velocities, as well as the sum of the final velocities, and record these values in Table 1.2.

6. Using the masses in Table 1.1, multiply your carts’ respective masses with their initial and final velocities to find corresponding momentums. Record the values in Table 1.3.

Section 2: Elastic Collision

Part A: m1 = m2

1. Record the masses of each cart in Table 2.A.1.

2. Place the red and blue carts at rest on the track, with the magnetic bumpers facing each other. The blue cart should be in the center of the track and the red cart should be on the left end.

3. Start recording and give the red cart a push toward the blue cart. Stop recording before either cart reaches the end of the track.

4. On the velocity vs. time graph, find the velocity of the red cart just before and just after the collision. The time just before the collision is most easily identified by finding the time  when the blue cart first begins to move. Record these values in Table 2.A.2.

5. The initial velocity of the blue cart is zero. Find the final velocity blue cart just after the collision, then record this value in Table 2.A.2.

6. Add together the sum of the initial velocities, as well as the sum of the final velocities, and record these values in Table 2.A.2.

7. Using the masses in Table 2.A.1, multiply your carts’ respective masses with their initial and final velocities to find corresponding momentums. Record the values in Table 2.A.3.

 

Part B: 2m1 = m2

1. Add mass to Cart 2 (blue cart) until it weighs twice as much as Cart 1 (red cart). To accomplish this you can use the  mass bar.

2. Record these new mass values in Table 2.B.1.

3. Repeat steps 2-7 from Part A, except now use the tables for Part B.

Part C: m1=2m2

1. Remove the extra mass on Cart 2 (blue cart) that you added in Part B.

2. Add mass to Cart 1 (red cart) until it weighs twice as much as Cart 2 (blue cart). To accomplish this you can use the  mass bar.

3. Record these new mass values in Table 2.C.1.

4. Repeat steps 2-7 from Part A, except now the tables for Part C.

Data

Section 1: (Perfectly) Inelastic Collision

Table 1.1: Cart masses

m1 (red cart) mass (kg) 0.2732
m2 (blue cart) mass (kg) 0.2712

Table 1.2: Velocities

  Cart 1 (red) Cart 2 (blue) Sum (1+2)
vi (m/s) 0.258 0  
vf (m/s) 0.129 0.129  

Table 1.3: Momentums (p=mv)

  Cart 1 (red) Cart 2 (blue) Sum (1+2)
pi (kg m/s)   0  
pf (kg m/s)      

Table 1.4: Kinetic Energies (KE=0.5mv^2=0.5p^2/m)

  Cart 1 (red) Cart 2 (blue) Sum (1+2)
KEi (Joules)   0  
KEf (Joules)      

Section 2: Elastic Collisions

Part A: m1 = m2

Table 2.A.1: Cart masses

m1 (red cart) mass (kg) 0.2732
m2 (blue cart) mass (kg) 0.2712

Table 2.A.2: Velocities

  Cart 1 (red) Cart 2 (blue) Sum (1+2)
vi (m/s) 0.121 0  
vf (m/s) -0.002 0.121  

Table 2.A.3: Momentums (p=mv)

  Cart 1 (red) Cart 2 (blue) Sum (1+2)
pi (kg m/s)   0  
pf (kg m/s)      

Table 2.A.4: Kinetic Energies (KE=0.5mv^2=0.5p^2/m)

  Cart 1 (red) Cart 2 (blue) Sum (1+2)
KEi (Joules)   0  
KEf (Joules)

      

Part B: 2m1 = m2

Table 2.B.1: Cart masses

m1 (red cart) mass (kg) 0.2732
m2 (blue cart) mass (kg) 0.5423

Table 2.B.2: Velocities

  Cart 1 (red) Cart 2 (blue) Sum (1+2)
vi (m/s) 0.397 0  
vf (m/s) -0.124 0.257  

Table 2.B.3: Momentums

  Cart 1 (red) Cart 2 (blue) Sum (1+2)
pi (kg m/s)   0  
pf (kg m/s)      

Part C: m1=2m2

Table 2.C.1: Cart masses

m1 (red cart) mass (kg) 0.5422
m2 (blue cart) mass (kg) 0.2712

Table 2.C.2: Velocities

  Cart 1 (red) Cart 2 (blue) Sum (1+2)
vi (m/s) 0.280 0  
vf (m/s) 0.082 0.365  

Table 2.C.3: Momentums

  Cart 1 (red) Cart 2 (blue) Sum (1+2)
pi (kg m/s)   0  
pf (kg m/s)      

Analysis

Section 1: (Perfectly) Inelastic Collision

We will use the tables from the data section to answer questions about which sum of variables is conserved and which is not conserved. Fill out the following table “Is it Conserved”, by deciding whether or not each variable sum is conserved or not. To decide, examine the Sum(1+2) column of each variable table above.

Table A.1: Is it Conserved?

Variable/Quantity Is it conserved? (is xi=xf?) [Y/N]
v: velocity  
p: momentum  
 

Section 2: Elastic Collisions

We will repeat the analysis from Section 1 on Section 2 data. Use the tables from Part A to complete the following table “Is it Conserved?”

Table A.2: Is it Conserved?

Variable/Quantity Is it conserved? (is xi=xf?) [Y/N]
v: velocity  
p: momentum  
 

Do you think this table would be different for Parts B and C? Explain why or why not:

 

Questions

1. In Section 2A,  , i.e. Cart 1 should come to a rest. Did your cart do this? If not, what is a reason why it may not have been perfectly at rest?

 

2. Why is it important to make certain we are using a level, frictionless surface?

 

3. In Section 1, some of the kinetic energy is lost after the collision. Where did the energy go?

 

Appendix (optional reading)

Full derivation of final velocities for elastic collisions

In an elastic collision, we can use the fact that both momentum is conserved and kinetic energy is conserved. We therefore have two equations:

 ,and

 .In our experiment, we assume that we know  and we know  . So our equations simplify:

 ,and .

To solve these equations, we first isolate  in the first equation by dividing through by  :

 .Now we can substitute this into the conservation of energy equation:

 .The fraction can be distributed throughout our parentheticals, and the term on the left side can be cancelled out:

 .Next, we move the remaining terms to opposite sides of the equality and divide by a factor of  :

 .Isolating  and cancelling the factor of  , we find:

 ,which gives the final result for  :

 .With an expression for  found, we substitute this back into the equation at the top of the appendix to solve for  :

 .This leads to the final derivation listed in the theory section for  ,

 .1 Department of Physics

 
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M4A1 Experiment: Electromagnetic Induction

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While completing the experiment Electromagnetic Induction, make sure to keep the following guiding questions in mind:

· Is the magnitude of the magnetic field the primary determinant in the Emf induced in the coil?  If not, then what is the primary determinate of the magnitude of the induced Emf?

· How is relative motion between the field and coil induced?  What controls do you have for changing the relative motion?  What is the relationship between the units of RPM and radians per second?

· How can ratios be used in an experiment when data is only available in the form of relative magnitudes?

To complete the experiment you will need to:

1. Be prepared with a laboratory notebook to record your observations.

2. Click the image to open the simulation experiment.

3. Perform the experiment as described.

4. Transfer your data and results from your laboratory notebook into the lab report template provided at the end of this experiment description.

5. Submit your version of the laboratory experiment report.

In your laboratory notebook, you will collect data, make observations, and ponder the questions posed within the lab instructions.  Thus, the notebook should contain all the data collected and analysis performed, which will be invaluable to you as you write the results section of your laboratory report.  Furthermore, the notebook should contain your observations and thoughts, which will allow you to address the questions posed, both for the discussion section in the laboratory report and in helping you to participate in the online discussion included in the module.

M4A1 Experiment: Electromagnetic Induction

 

PART I – Faraday’s Law and Relative Motion

Start the simulation “Faraday’s Electromagnetic Lab ” by clicking on the image below:

http://phet.colorado.edu/sims/faraday/faraday_en.jnlp

http://phet.colorado.edu/sims/faraday/faraday_en.jnlp

 

· Select the tab labeled “Pickup Coil.”

· Move the bar magnet to various static (“nonmoving”) positions.

Note that any static position from which the magnet seems to induce a potential in the coil seems to cause the bulb to shine brightly. Try various static positions, including near and far positions. Use the simulation controls to flip the field. Note your observations in your laboratory notebook. Pick other controls available in the simulation to vary the field. What do your observations imply about the magnitude and direction of the magnetic field in inducing an electromotive force in the pickup coil? Do your observations indicate any other factors that might induce an EMF in the pickup coil, and thus, cause the bulb to shine?

Note any factors that will induce an EMF in your notebook. Investigate the general relationship between the magnitude of the bulb brightness and the particular factor you are considering. Your investigation should indicate whether bigger, faster, further, or more causes the bulb to burn brighter than the converse.

Part II – Parameters effecting Generator Performance

· Select the generator tab of the simulation.

· In the simulation, controls select the voltmeter to replace the bulb.

You will note that the voltmeter scale is not calibrated, but that you can still compare various potential readings by counting “tick marks” on the face of the meter. Using this scale to collect data, vary the relationship between the maximum electromotive force EMFmax produced and the various parameters in the generator equation, EMF = ωNBAsin(ωt). Specifically, vary the angular frequency (ω) (by adjusting the water flow through the spigot on the left), number of loops (N), and area of the loop (A). Choose one parameter and produce a plot of EMFmax vs. the parameter. Be sure to use at least 10 data points. Record the results in your laboratory notebook.

PART III – Calibrating the Galvanometer

The voltmeter scale is uncalibrated in part because we are missing two values: 1) the average of the peak magnetic field strengths across the surface bounded by the loops in the pickup coil, and 2) the maximum area of the loops of the pickup coil.

Given that the maximum area of the loop is 0.75m², and the maximum magnetic field strength at the location of the coil is 0.6 T, you should be able to find the value of a single tick mark on the voltmeter scale.

In your laboratory notebook write down a detailed procedure for doing so. Carry out this measurement with angular speeds of 25, 50, and 100 RPM. Are these values comparable? Do they need to be for the meter to be useful? Why or why not?

1. The Lab Report

Click here for a lab report template [DOCX file size 12.6 KB], and click here for an explanation of each lab component [DOCX file size 17.4 KB].

· Write an introduction of at least 1 page in length. The introduction should showcase your understanding of electromagnetic induction.

· Write a methods section describing in your own words the experimental procedure used to complete each activity. Do not copy and paste, or simply repeat the directions given in the course materials.

· Write a results section. This section should begin with a paragraph containing any hypotheses formed and tested during the conduct of the laboratory. This section should also contain any data collected, sample calculations, analysis, and plots of the data or results.

· Write your discussion section specifically addressing how your results did or did not support any hypothesis used in this laboratory.

· Write your conclusion. This section should be brief, at most, one or two paragraphs; connect the discussion with the information contained in the introduction.

· Write the abstract. While this is the first section of your lab report, it should be written last. This section should be written in the past tense, in the third person, and should be a summary of the entire laboratory report.

Compose your work using a word processor (or other software as appropriate) and save it frequently to your computer. When you’re ready to submit your work, click Browse My Computer and find your file. Once you’ve located your file click Open and, if successful, the file name will appear under the Attached files heading. Scroll to the bottom of the page, click Submit and you’re done. Be sure to check your work and correct any spelling or grammatical errors before you post it.

You will be evaluated on the validity of your recorded results and the completeness and quality of your presentation of those results within the experiment report, based on the Lab Report Grading Rubric [PDF file size 63.7 KB].

 
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Physics Lab Assignments

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Transcript: PHY 21041 Lab 12

For this lab, you need to do a little bit of work ahead of time.  You need a pair of glasses,  like old people would wear.  Not prescription glasses, not bifocals‐ they wouldn’t work,  just ordinary, plain vanilla reading glasses.  If you’re too embarrassed to borrow them  from somebody, just go to Goodwill or something like that to get the cheapest reading  glasses you can find.  So go ahead and get some glasses and come right back!    Unidentified voice: Hey, you young whippersnapper!  Come back here with my glasses!   And get off my lawn!    Unidentified voice: Sorry, he made me do it! I’ll be right back.    Unidentified voice: Here you go!  Gotta run!    Oh, Thank you! I guess.   Now all we need is a place to set this up.  We need a really dark room.  I wonder where  we could find one of those.  Well, this is convenient.  Let’s go on in.     We found our dark room, now.  Here are the glasses my student just got for me.  And  I’m using my laptop as a light source.  I found a big, red arrow there as an image that we  can use.  I’m going to set it right here at the end of this long table, with the screen  straight up and down.  Way down there, at the other end of the table, I have the piece  of index card that came from your packet.  I have it attached to your book end down  there.  I have another book end right here that I can use to steady the lens so the image  will be sharp and clear when I move it down there.     Let’s see what you would do now in the lab.  I’m going to hold the glasses, covering one  lens.  Only one lens is being used.  I’m going to start a long distance away from the  computer screen.  The most common problem is in doing this lab is starting too close.   So start a good distance away from the computer screen.  And what I’m going to do now  is move the lens further and further away until I see an image come to focus on my card  over here.  And there it comes, we’re almost there.  And there is a nice sharp image in  the card.  You’ll need to then measure, this distance from the lens to the computer,  that’s called the object distance, DO, because the computer screen is the object.  We’ll  also measure from the lens to the card.  That’s the image distance, DI.      From the instructions in Blackboard learn, you’ll see how to calculate the focal length of  this lens using DO and DI.   What I want you to do is several different trials like this,  where you will move the cardboard screen and then move the lens to a new place to  refocus again, in each case measuring DO and DI.

 
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Part A: STANDING WAVES ON A STRING Using PhET simulation

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Part A: STANDING WAVES ON A STRING Using PhET simulation

(Part A: STANDING WAVES ON A STRING Using PhET simulation) 12/27/2019

OBJECTIVE

To study standing waves on a string and see the effects of changing the tension in the string,

EQUIPMENT

PhET Simulation Wave on a String: https://phet.colorado.edu/en/simulation/wave-on-a-string

You can also reach this simulation by going to PhET, and looking for Wave on a String.

 

Theory: Standing Waves in Strings

For any wave with wavelength λ and frequency f, the speed, v, is

v = λf (1)

The speed of a wave on a string is also related to the tension in the string, T, and the linear density (=mass/length), μ, by

v2 = T/μ = λ2f2 (2)

L is the length of the string and n is the number of segments, antinodes, or harmonics. Since a segment is 1/2 wavelength then

λ = 2L/n where n = 1, 2, 3, … (3)

Solving Equation 2 for the tension yields:

T = μλ2f2 (4)

Which can also be written as:

(5)

PROCEDURE

Constant Tension

1. Open the software. Select: Oscillate, Amplitude = 0.10 cm, Damping = 0, Tension = Lowest, Fixed End.

2. Turn on the oscillator by pressing the large blue button with the arrow. You will see the wave going from left to right, hit the fixed end and reflect. The reflected waves will interfere with the waves going to the right.

3. Now adjust the frequency in the Signal Generator until you get a standing wave in one segment (i.e. the first harmonic). Note this frequency, and measure the wavelength by using the ruler tool. (Part A: STANDING WAVES ON A STRING Using PhET simulation)

4. Increase the frequency gradually until you obtain a standing wave in the 2nd, 3rd, 4th, and 5th harmonic. Record each frequency and wavelength.

5. Calculate the wavelength by using equation (3).

6. Calculate the velocity of the waves by using equation (1)

7. Change the oscillator to Pulse. Keep the pulse width small. Measure the time taken by the pulse to travel from the left to the right ends, and hence calculate the velocity of the pulse in the string. Repeat three times and take the average. Use this value as a second value of the speed of the wave.

8. Calculate the percent difference between the two speeds.

Number of Harmonic

 

 

 

( n )

 Number of nodes Wavelength

λ = 2L/n

 

 

 

( m )

 Frequency

f

 

 

 

( Hz )

 Speed of wave

V = λ*f

 

 

( m/s )
1
2
3
4
5

9. Repeat for the other two available tensions of the string. Case A: Lowest Tension

DATA TABLE

Length of the string: _________

Speed of the wave

Trial number Time for pulse to reach other end Speed of the wave
Average speed of the wave

Length of the string: ____________

Case B: Medium Tension

Number of Harmonic

 

 

 

( n )

 Number of nodes Wavelength

λ = 2L/n

 

 

 

( m )

 Frequency

f

 

 

 

( Hz )

 Speed of wave

V = λ*f

 

 

( m/s )
1
2
3
4
5

 

Speed of the wave

Trial number Time for pulse to reach other end Speed of the wave
Average speed of the wave

 

Length of the string: ____________

Case C: Highest Tension

Number of Harmonic

 

 

 

( n )

 Number of nodes Wavelength

λ = 2L/n

 

 

 

( m )

 Frequency

f

 

 

 

( Hz )

 Speed of wave

V = λ*f

 

 

( m/s )
1
2
3
4
5

 

Speed of the wave

Trial number Time for pulse to reach other end Speed of the wave
Average speed of the wave

Part B E-39-0 Electric Charges and Electric Fields ONLINE

6-21-2020 Adapted from manual from Dr. Kam Chu

 

Objective

To study the electric field and electric potential around different charges.

 

Equipment

PhET Simulation:

https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html

 

Theory

There is an electric field surrounding a charge, in which another charge would experience an electric force. The strength of the electric field at a distance from a point charge is given by:

(1)

Where is the Coulomb Constant, q is the charge, and r is the distance from the charge. The unit vector points away from a positive charge, and towards a negative charge. (Part A: STANDING WAVES ON A STRING Using PhET simulation)

 

The electric potential due to a point charge is given by the equation:

(2)

Where is the electric potential (in volts), and is a scalar quantity.

 

In this Lab, we will use a PhET simulation to study the electric field and electric potential surrounding single and multiple point charges.

 

Procedure

Play with the simulation (Charges and Fields) and get oriented with all the different options. This should help you understand the lab better. Note that you have positive and negative point charges, an electric field sensor (yellow circle), a tape measure and a voltmeter, that also makes the equipotential lines. For each case, take a screenshot and attach with your report. You may alsoturn on ‘gridlines’ if desired. Each small square of the grid is 10 cm wide and high. (Part A: STANDING WAVES ON A STRING Using PhET simulation)

 

Activity 1: Electric Field Lines and Equipotential Lines

1: Have one positive and one negative charge placed symmetrically in the field. Get the Electric field lines. Use the voltmeter to draw about ten equipotential lines (Figure 1 shows a related situation with a few equipotential lines)

2: Repeat with both charges being negative.

3: Repeat with both charges being positive.

4. Repeat with 4 positive charges (on top of each other, to create 4q) and one negative charge.

5. Parallel Plates: Put a large number of positive charges in a straight row (to look like a solid line). Make a negative line in the same way (parallel to the first). As an example, see figure 2. Get the electric field lines and Equipotential Lines between and surrounding the parallel plates.

6. Attach screenshot of the simulations in your report. Figure – 1

Figure-1: Parallel “plates”. 

 

 

 

 

 

 

ACTIVITY 2

1) Turn on ‘gridlines’.

2) Select positive point charge of any magnitude (you do this by placing the point charges on top of each other). Place the charge at the intersection of two thick gridlines, somewhere in the left half of the screen.

3) Use the tape measure and Voltmeter to find the voltage at different locations along the horizontal line on which the charge is placed. Enter values in Table 1.

4) Plot a graph in Excel between the voltage (y-axis) and the distance (x-axis).

5) Use Excel to determine the value of the Coulomb Constant (see eqn. (2). Find the percent error between the calculated and accepted values.

6) Use the tape measure and the yellow Electric Field sensor to measure the electric field at different distances in the horizontal direction from the charge. Enter the data in Table 2.

7) Plot a graph in Excel between the Electric Field (on y-axis) and distance (on x-axis)

8) Use Excel to determine the value of the Coulomb Constant (see eqn. (1)). Find the percent error between the calculated and accepted values.

9) Attach the screenshots, graphs and calculations to your report. (Part A: STANDING WAVES ON A STRING Using PhET simulation)

DATA

 

Table 1

Charge = _________

 

1 2 3 4 5 6 7
distance
voltage

 

 

Value of k found from the graph: ___________

Percent error in k: ________________

 

Table 2

Charge = __________

1 2 3 4 5 6 7
distance
Electric Field

 

 

Value of k found from the graph: ___________

 

Percent error in k: ________________

 

Part C E-35-O CAPACITORS IN CIRCUITS ONLINE LAB

7/1/2020

OBJECTIVES

The purpose of this lab will be to determine how capacitors behave in R-C circuits by measuring the time for charging and discharging. The manner in which capacitors combine will also be studied.

 

EQUIPMENT

PhET interactive simulation tool [Circuit Construction Kit: (AC+DC) – Virtual Lab]

https://phet.colorado.edu/en/simulation/legacy/circuit-construction-kit-ac-virtual-lab

 

PROCEDURE

1. Open the simulation by ctrl+click the link, or copy paste the link to the browser. The simulation should look like that shown in Fig.6

2. Since this simulation is in java (and not web based as some of the others), you may have to download the simulation. If you cannot run the simulation, you may need to follow the following PhET help guidelines: https://phet.colorado.edu/en/help-center/running-sims

Then click “Why can Irun some of the simulations but not all?”

3. Run the simulation, and you will see a page like that shown in Fig.7.

4. You would not set up the circuit. For assistance in setting up the circuit, see the manual: 00PhET Simulation Tool Instructions for Electric Circuits Labs.

5. This experiment requires you to measure the voltage as a function of time. The timer can be easily controlled by using the Pause/Play button (►) and/or the step button (|►) (these are at the bottom of the page).

 

 

 

 

 

 

 

 

Figure 6. Figure 7.

Case-A: charging the capacitor.

1. Set up the circuit as shown in figure 8. Once set up, it should look something like that shown in figure 9.

2. Set the resistance to 100 Ω, capacitance to 0.05 F, and Battery to 10.0 V.

3. Before charging the capacitor, make sure that it has no charge (the voltmeter reads zero). Otherwise you need to discharge the capacitor first until the voltage across the capacitor becomes zero. (Part A: STANDING WAVES ON A STRING Using PhET simulation)

4. Put switch S1 in the ON state and switch S2 to the OFF state.

5. Set the Pause/Play button (►) to pause and the timer to zero. Before 5 seconds, use the step button (|►) to increase time by 0.5 second intervals and record the voltage values in Table I. After 5 seconds, use the Pause/Play button (►/||) to record the voltage at around 7.00, 10.0, 15.0, 20.0, and 25.0 seconds.

6. Using equation (5), obtain the charge at each time, and enter in Table 1.

7. Draw a graph between charge on y-axis and time on x-axis. It should look like Fig. 3.

8. Use the known values of resistance and capacitance to calculate the time constant and the maximum charge by using eqn. (2) and eqn. (3), and enter in Table 2.

9. Calculate the charges equal to one time constant, two time constants, and five time constants and enter in Table 2. Compare these with the experimental values using % error. Put your calculation in the table II.

C

 

 

Figure 8

 

 

 

Volt-meter

 

 

 

 

 

 

 

 

 

 

Figure 9.

 

Case-B: Discharging capacitor

1. Set up the circuit as shown in figure 8.

2. Set the resistance to 100 Ω, capacitance to 0.05 F, and Battery to 10.0 V.

3. Before discharging the capacitor, make sure the capacitor has been fully charged (the voltmeter reading is very close to 10.0 V).

4. Set switch to off and switch to on.

5. Set the Pause/Play button (►) to pause, and the stopwatch to zero. For time less than 5 seconds, use the step button (|►) to increase time by 0.5 second intervals. Record the voltage values in Table 3. After 5 seconds, use the Pause/Play button (►/||) to record the voltage at about 10.0, 15.0, 20.0, and 25.0 seconds.

6. Using equation (5), obtain the charge at each time, and enter in Table 3.

7. Draw a graph between charge on y-axis and time on x-axis. It should look like Fig. 5.

8. Use the known values of resistance and capacitance to calculate the time constant and the maximum charge by using eqn. (2) and eqn. (3), and enter in Table 4.

9. Calculate the charges equal to one time constant, two time constants, and five time constants and enter in Table 4. Compare these with the experimental values using % error. Put your calculation in the table II.

Case-C: Capacitors in Series.

1. Set up the circuit as shown in figure 10.

2. Set the resistance to 100 Ω, each capacitance to 0.05 F, and Battery to 10.0 V.

3. Before charging the capacitor, make sure that it has no charge (the voltmeter reads zero). Otherwise you need to discharge the capacitor first until the voltage across the capacitor becomes zero.

4. Put switch S1 in the ON state and switch S2 to the OFF state.

5. Now calculate the value of the time constant by using the equation for sum of capacitors in series.

6. Start charging the capacitors and note the voltage difference across both capacitors. Note the time it takes for the voltage to reach 63.2 % of Vmax. This is the measured value of time constant. Note this in Table 5.

7. Now charge the capacitors to full charge, and by using proper switching, measure the time for the voltage across them to fall BY 63.2% of Vmax. This is the measured time constant for discharging the capacitors.

8. Compare the measured and calculated values of the time constant for capacitors in series. (Part A: STANDING WAVES ON A STRING Using PhET simulation)

 

 

 

 

Figure 11

 

 

Volt-meter

 

 

 

 

C1

C2

Volt-meter

 

 

C2

C1

 

 

 

 

 

 

 

Figure 10

 

 

Case-D: Capacitors in parallel.

1. Set up the circuit as shown in figure 11.

2. Set the resistance to 100 Ω, each capacitance to 0.05 F, and Battery to 10.0 V.

3. Repeat the steps needed to measure the time constant while charging and while discharging, and compare with the calculated value for capacitors in parallel.

4. Enter the results in Table 5.

 

DATA

Case-A: Data for charging a single capacitor

 

Table-1

Resistance R = _________ Capacitance C = ________

 

Time

(s)

 Measured Voltage (VC) Charge on Capacitor

q(t)

(eqn. (5)

 Time (s) Measured Voltage (VC) Charge on Capacitor q(t)

(eqn. (5)

 Time (s) Measured Voltage (VC) Charge on Capacitor q(t)

(eqn. (5)
0.50 3.00 7.00
1.00 3.50 10.0
1.50 4.00 15.0
2.00 4.50 20.0
2.50 5.00 25.0

 

 

Make a graph between q(t) and time.

 

Table 2

 

Maximum Charge from eqn (2) = Q = ___________

RC time constant from eqn (3) = τ = ___________

 

Calculated value

eqn (1)

 Experimental value

eqn (5)

 % error
Charge at t = 1 τ
Charge at t = 2 τ
Charge at t = 3 τ

 

 

 

Case-B: Data for Discharging a single capacitor

 

Table-3

Resistance R = _________ Capacitance C = ________

 

Time

(s)

 Measured Voltage (VC) Charge on Capacitor

q(t)

(eqn. (5)

 Time (s) Measured Voltage (VC) Charge on Capacitor q(t)

(eqn. (5)

 Time (s) Measured Voltage (VC) Charge on Capacitor q(t)

(eqn. (5)
0.50 3.00 7.00
1.00 3.50 10.0
1.50 4.00 15.0
2.00 4.50 20.0
2.50 5.00 25.0

 

 

Make a graph between q(t) and time.

 

 

Table 4

 

Maximum Charge from eqn (2) = Q = ___________

RC time constant from eqn (3) = τ = ___________

 

Calculated value

eqn (4)

 Experimental value

eqn (5)

 % error
Charge at t = 1 τ
Charge at t = 2 τ
Charge at t = 3 τ

 

 

 

Case C and D: Data for Two Capacitors in Series and Parallel:

 

Table 5:

Resistance: ____________ Capacitance 1: _____________ Capacitance 2: _____________

 

Type of Circuit

Capacitors in:

 Calculated values of

τC and τD

 Measured Charging time τC Measured Discharging time τD Percent error in time of charging Percent error in time of discharging
Series
Parallel

 

 

τC : Time constant for charging

τD : Time constant for discharging

 

Part D Lab 2 Ohm’s Law

 

Objective

Learn to build a simple circuit with one resistor and one DC source.

Use PhET interactive simulation tool (Circuit Construction Kit AC Prototype) to build circuits and verify Ohm’s Law.

Theory

Ohm’s Law states that the electric current passing through a resistor with resistance is proportional to the voltage (electric potential difference) across the resistor and inversely proportional to the resistance

 

Equipment

Ⓐ

 

 

 

Figure-1

PhET interactive simulation tool (Circuit Construction Kit: DC – Virtual Lab)

https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab

For guidance on how to use the simulation, tool, see PhET Simulation Tool Instructions for Electric Circuits Labs.

 

Procedures

1. Build the circuit as shown in Figure 1 using the PhET Simulation Tool.

2. Set the DC Power Source to 12.0 V.

3. Create three resistors 10.0 Ω, 20.0 Ω, and 30.0 Ω. Putting each resistor into the circuit one at a time, measure voltage using the voltmeter and record the values on Table 1. Note that the volt-meter should be parallel with the resistor.

4. With the power source still set at 12.0 V, measure the current of each resistor and record the values on Table 1. The ammeter should be in series with the resistor. You must first cut the circuit and open it with two disconnected ends and then plug in the ammeter. Please refer to “PhET Simulation Tool Instructions for Electric Circuits Labs” for how to measure current.

5. Avoid the common mistake of connecting the ammeter directly to the power supply’s two terminals.

6. Compare the calculated and measured currents in Table 1 and find the percentage difference.

7. Put the 10.0 Ω resistor in the circuit and increase the voltage of the power supply from to using increments. Using the method outlined in step 4, measure the current at each step. Record the voltage and current values in Table 2.

8. Plot the voltage-current curve and find the slope of the line. The slope of the line will be the resistance.

9. Compare the measured with the known values of the resistance values and find the percentage error.

 

In you report, include screenshots of the circuits that you make for doing this Lab. (Part A: STANDING WAVES ON A STRING Using PhET simulation)

Data Table 1

DC Power Source: 12.0 V

 

Resistance Measured Voltage Calculated Current (Equation 1) Measured Current % difference in the current
10.0 Ω
20.0 Ω
30.0 Ω

 

 

Data Table 2

Resistance: 10.0 Ω

 

Voltage

(volt)

 Measured Current

(ampere)

 Slope (equals resistance)

(ohm)

 % error in resistance
1.00 V
2.00 V
3.00 V
4.00 V
5.00 V

 

 

Part E Series and Parallel Circuit

(Using PhET Simulation Tool)

Objective

1. Learn to build up series circuit and a parallel circuit with three resisters.

2. Use PhET interactive simulation tool (Circuit Construction Kit AC Prototype) to build the circuits and Verify Ohm’s Law

Theory

The relations for two resisters in series and parallel circuits are the following:

Series Circuit Parallel Circuit

 

 

 

 
 

 

 

  

 

 
 

 

 

 

 

 

 

 

 

 

 

 

Figure 1 Two resister in series

  

 

 

 

 

 

 

 

 

Figure 2 Two resister in parallel

 

Equipment

PhET interactive simulation tool (Circuit Construction Kit: DC – Virtual Lab)

https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab

 

Procedures

 

Build the circuit as shown in Figure 1 by using PhET Simulation Tool

 

1. Click the above http link, you will see

 

2. Click ▲, you will see

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3. Now you build your circuit by using “wire”, “Battery” and “Resistor”

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4. You can tap the circuit elements to change it value by adjust

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. You can also toggle between the battery and the battery symbol as shown above.

6. Use the circuit board, build the series circuit by using three resisters as shown in the following figure 3: set up , , ,

 

 

 

 

 

Figure 3

 

 

 

7. Measure the voltage across each resister, the voltage across over the two and (resister) and the voltage across over all the resisters (). Record the values on the table 1.

 

How to use the circuit board tool Voltmeter to measure the voltage

 

Simple drag the Voltmeter to the necessary location as shown in the following figure.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8. Using Ohm’s law calculate the currents for each resister and put the values on table 1.

9. Using circuit board tool Ammeters measure the current passing through each resister and record the values on the table 1. Note that the Ammeters should be in series with the resister. (The figure below show you how to cut a circuit open and then put the Ammeters)

 

 

 

 

 

 

 

 

 

 

 

 

10. Compare the current in table 1, and find the percentage difference.

11. Use the circuit board, build the parallel circuit by using three resisters as shown in the following figure 4.

 

 

 

 

 

 

 

 

 

 

Figure 4

 

 

 

 

12. Repeat procedures from 7 to 10, record the data in table 1, and find the percentage difference.

 

Data Table 1

Resistance: :___________ :____________ :____________

 

Series Parallel
Measured Voltage  

(Ohm law)

 Measured Current % difference Measured Voltage  

(Ohm law)

 Measured Current % difference

 

 

Your Lab Report Should Include the Following

 

1. Lab theory

2. Your build circuit photo

3. Procedures

4. Your circuit setup photo which shows voltage [across the two and (resister)] measurement; and circuit setup photo which shows current [pass through the two resistor and (resister)] measurement.

5. Data Table 1

6. Conclusion

Part F Combination of Series and Parallel Circuit

(Using PhET Simulation Tool)

Objective

3. Learn to build up a combination of series and parallel circuit with three resisters.

4. Use PhET interactive simulation tool (Circuit Construction Kit AC Prototype) to build the circuits and Verify Ohm’s Law

 

Theory

Combination of Series and Parallel Circuit
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1 Two resister in series

  

 

 
 

 

 

 

 

Equipment

PhET interactive simulation tool (Circuit Construction Kit: DC – Virtual Lab)

https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab

 

Procedures

 

Build the circuit as shown in Figure 1 by using PhET Simulation Tool

 

13. Click the above http link, you will see

 

14. Click ▲, you will see

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15. Now you can build your circuit by using “wire”, “Battery” and “Resistor”

 

 

 

 

 

 

 

 

 

 

 

 

 

 

16. You can tap the circuit elements to change it value by adjust

 

 

 

 

 

 

 

 

 

 

 

 

17. You can also toggle between the battery and the battery symbol as shown above.

18. Use the circuit board, build a combination of series and parallel circuit by using three resisters as shown in the following figure 2: set up , , ,

 

 

 

 

 

 

Figure 2

 

 

 

19. Measure the voltage across each resister, and the voltage across over the two and (resister) Record the values on the table 1.

 

How to use the circuit board tool Voltmeter to measure the voltage

 

Simple drag the Voltmeter to the necessary location as shown in the following figure.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20. Using Ohm’s law calculate the currents for each resister and put the values on table 1.

21. Using circuit board tool Ammeters measure the current passing through each resister, and the current going through the two and (resister). Record the values on the table 1. Note that the Ammeters should be in series with the resister. (The figure below show you how to cut a circuit open and then put the Ammeters)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

22. Compare measured current in column 3 and calculated current in column 4 in the table 1, and find the percentage error.

 

Data Table 1

 

Resistance: :___________ :____________ :____________

 

 

1 2 3 4 5
Measured Voltage Calculated Current

(Using Ohm’s Law)

 Measured Current Calculated Current

(Using Equation 1-6)

 % error (compare column 3 and 4)

 

 

Your Lab Report Should Include the Following

 

7. Lab theory

8. Your build circuit photo

9. Procedures

10. Your circuit setup photo which shows voltage [across the two and (resister)] measurement; and circuit setup photo which shows current [pass through the two resistor and (resister) measurement.

11. Data Table 1

12. Calculation details in column 4

13. Conclusion

 

Part G E-34-O KIRCHHOFF’S RULES ONLINE LAB

7/01/2020

 

OBJECTIVE

The purpose of this lab will be to experimentally demonstrate Kirchhoff’s Rules for electrical circuits.

 

EQUIPMENT

PhET interactive simulation tool (Circuit Construction Kit: DC – Virtual Lab):

https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab

For an introduction on using the PhET Circuit Construction simulation, see: 00-PhET Simulation Tool instructions for Electric Circuits Labs.

 

THEORY (Part A: STANDING WAVES ON A STRING Using PhET simulation)

Electronic circuits that cannot be reduced to simple series of parallel circuits can be analyzed by different methods. As an example, consider the circuit of figure 1. The currents and voltage drops across the resistances cannot be found by a simple application of Ohm’s Law. In this circuit, points A and D are called Junctions, since more than two wires connect there. A closed loop is any path that starts at some point in the circuit, passes through the elements of the circuit, and arrives back at the same point, without passing through any element more than once. There are three such closed loops in the circuit of Figure 1. These are Loop 1: A-B-C-D-A, Loop 2: A-D-E-F-G-A, and Loop 3: B-C-D-E-F-G-A-B. The junctions and loops are used in two Kirchhoff’s rules to analyze the circuit.

KCR- Kirchhoff’s Current Rule: The sum of the currents entering a junction = sum of currents leaving a junction. Or equivalently: the net current entering a junction is zero.

KVR-Kirchhoff’s Voltage Rule: The algebraic sum of the voltage changes around any closed loop is zero.

We would usually know the values of the battery voltages and resistances. As a first step, we label and assign directions (arbitrarily) to the currents in each section of the circuit (i.e. between each junction). We then write the junction equation (assuming a current entering the junction is positive, and leaving the junction is negative) at node D as:

i1 + i3 – i2 = 0 (1)

We now traverse the closed loops in any direction (clockwise or counter-clockwise, the resulting equations are equivalent) and add up all the changes in the voltages and set them to zero, i.e.

ΣΔV = 0 (2)

The voltage change across a resistor is found by Ohm’s Law as

ΔV = I R (3)

The sign of ΔV is positive if we are crossing the resistance in a direction that is against the direction of the current in that resistor, and it is negative if we go across the resistor in the same direction as the current. The ΔV across the battery is positive if we cross it from its negative to its positive side. With these, the equations for the three loops become:

Loop 1 (starting at the point A and going clockwise):

V1 – i1*R1 – i1*R2 + i3*R3 = 0.0 (4)

 

Loop 2 (starting at A and going clockwise):

-i3*R3 – i2*R4 + V2 – i2*R5 = 0.0 (5)

Loop 3 (starting at A, and going clockwise):

+V1 – i1*R1 – i1*R2 – i2*R4 + V2 – i2*R5 = 0.0 (6)

Note that equation (6) is simply the sum of equations (4) and (5), and is therefore not an independent equation. The same would apply to the junction rule applied at node A. So the useful (or independent) number of Junction equations that we can use are one less than the number of junctions, and the Loop equations are one less than the number of loops.

We then simultaneously solve equation (1) and any two out of equations (4), (5) and (6) to obtain the values of the currents i1, i2 and i3. In case any of the currents comes out to be negative, it simply means that we had choses then wrong direction for that current.

 

 

 

 

 

 

 

 

 

 

PROCEDURE (Part A: STANDING WAVES ON A STRING Using PhET simulation)

1 Select five resistors and measure and note their resistances. Label them as R1, R2, … , R5. Select resistors that are in the range of 10.0 Ω to 100.0 Ω.

2 Connect the resistors on the PhET simulation to make the circuit as shown in Figure 1. Attach the two batteries to appropriate points on the circuit. Set their voltages between 6.0 to 10.0 volts each. (The two voltages may or may not be the same). Note the positions of the resistors R1, R2, … R5. Measure the voltages across the batteries and note these as V1 and V2 in the Data Sheet.

3 Using the values of the resistances and battery voltages, calculate the currents i1, i2 and i3 by using the two Kirchhoff’s Rules. Use the same notation and directions of the currents as used in Figure 1. Use the calculated currents to calculate the potential difference across each resistor by using Ohm’s Law.

4 Once the calculations are done, you have an idea of what values to expect. First measure the voltages across each of the resistors and note it.

5 Now measure the currents i1, i2 and i3. For this you would need to break the circuit and insert the ammeter in series with the wires to complete the loop.

6 Calculate the percent errors in the calculated and measured values of the currents and voltages. Check to see if the Kirchhoff’s Junction rule and Loop Rules are verified.

 

DATASHEET: KIRCHHOFF’S RULES

 

 

V1 =
V2 =

 

 

 

RESISTANCE CURRENT VOLTAGE
CALCULATED MEASURED % ERROR CALCULATED MEASURED % ERROR
R1 =
R2 =
R3 =
R4 =
R5 =

 

 

 

Part H: Geometrical Optics Using PhET SIMULATIONS (Part A: STANDING WAVES ON A STRING Using PhET simulation)

Rev 3-14-2020

 

OBJECTIVE

To study the reflection of light on flat and curved surfaces, and refraction of light though different shapes, and to find the focal length of a convex lens.

 

EQUIPMENT

PhET simulation Bending Light: https://phet.colorado.edu/en/simulation/bending-light

 

PhET simulation Geometric Optics: https://phet.colorado.edu/en/simulation/legacy/geometric-optics

 

You can also get to the simulations by entering in your browser: Phet, then select Physics. Then select Bending Light, and Geometric Optics simulations.

 

PROCEDURE (Part A: STANDING WAVES ON A STRING Using PhET simulation)

The procedure for all experiments will be to track a laser beam as it reflects or refracts. In the simulations that we will use, we have a laser that can be turned on or off by clicking the red button on it. It can also be moved and rotated. The laser will give a narrow ray of light which we will follow as it reflects or refracts. This can be done for several points in the beam’s path.

 

In most cases, you would need to measure the angle, which is done from the normal to the surface. You can turn on the normal by selecting it in one of the menu boxes on the page. You can measure the angle by using the protractor tool. Complete the Results section at the end.

 

CASE A: Reflection from a Plane Mirror (see figure 1)

1. After opening the simulation, select “INTRO”.

2. Select the material where the laser is as “AIR”, and that on the lower side as “WATER”.

3. Set the laser to any arbitrary angle. Turn on the laser.

4. Use the Protractor to measure the angle of the incident ray and angle of the reflected ray (this is dimmer than the incident ray). (ignore the ray going into the water). Repeat for different angles.

5. Repeat for AIR and GLASS as the materials.

6. Enter the results in Table A, and verify that the angle of incidence = angle of reflection.

CASE B: Refraction (see figure 2)

1. After opening the simulation, select “INTRO”.

2. Select the material where the laser is as “AIR”, and that on the lower side as “WATER”.

3. Set the laser to any arbitrary angle. Turn on the laser.

4. Use the Protractor to measure the angle of the incident ray and angle of the refracted ray (i.e. the one entering the water). (ignore the reflected ray). Repeat for different angles.

5. Repeat for AIR and GLASS as the materials.

6. Repeat with AIR and MYSTERY A as the two materials.

7. Enter the results in Table B, and calculate the refractive indices of water, glass and Mystery A by using equation 1.

 

CASE C: Refraction Again (see figure 7)

1. After opening the simulation, select “PRISM”.

2. From the bottom panel, select the Square. Set Reflections Off. Turn on Normal.

3. Select the Environment as AIR. Select Objects as GLASS.

4. Set the laser to any arbitrary angle, pointing to the square. Turn on the laser.

5. Use the Protractor to measure the angle of the incident ray and angle of the refracted ray (i.e. the one entering and inside the square). Make sure that the ray inside the square does not reflect form the side surface.

6. Use these angles to calculate the refractive index of the material by using equation 1. Repeat with different angles.

7. Repeat for MYSTERY B as the material of the square.

8. Enter the results in Table C.

CASE D: Total Internal Reflection (Part A: STANDING WAVES ON A STRING Using PhET simulation)

1. After opening the simulation, select “INTRO”.

2. Select the material where the laser is as “WATER”, and that on the lower side as “AIR” (i.e. the laser beam is going from water into air)

3. Set the laser to a small angle (i.e. close to the normal). Turn on the laser.

4. Increase the angle slowly and observe the refracted ray. At some angle, the refracted ray will become parallel to the water-air surface. Beyond this point, when the angle is further increased, there is no refracted ray, only a reflected ray. This is Total Internal Reflection. The angle that the incident ray makes at the point at which the refracted ray becomes parallel to the glass surface (i.e. angle of refraction = 90), is called the Critical Angle. Use the Protractor to measure the angle of incidence at this point. Use equation 3 to compare the calculated and measured values of the Critical Angle.

5. Repeat to find the critical angle for the GLASS – AIR interface.

6. Enter the results in Table D.

 

CASE E: Total Internal Reflection Again (see figure 6)

1. After opening the simulation, select “PRISM”.

2. Select the semi-circular object, and bring it to the middle of the screen. Its straight side should be vertical.

3. Select the Environment as Air, and semi-circular object as Glass. Turn on Normal. Turn off Reflections.

4. Turn on the laser. Set the laser to an angle about 40° with the horizontal.

5. Now place the cursor in the object, with left click hold the object and move it (it should not rotate) to a position so that the laser beam entering it is at zero degrees to the surface. This is when the beam is directly over (i.e. parallel to) the normal. It will now be exiting the object from center of the flat side, which is also the center of the circle forming the curved side. Now rotate the Object by holding it from the little thing at its bottom. The object must not move, only rotate. This will rotate it about its center so that the beam is always exiting from the center of the flat side.

6. Keep rotating the object slowly, until the exiting beam is parallel to the flat surface. If you turn it a bit more, the beam will have Total Internal Reflection. Use the protractor to measure the angle on incidence inside the object at the flat surface at the point of Total Internal Reflection. The angle of refraction should be 90°. Use equation 3 to compare the calculated and measured values of the Critical Angle.

7. Repeat for Mystery A. Use the refractive Index found in Case B for calculating the percent error.

8. Enter the results in Table E.

 

CASE F: Refraction Light Ray Shift (see figure 7)

1. After opening the simulation, select “PRISM”.

2. From the bottom panel, select the Square. Set Reflections Off. Turn on Normal.

3. Select the Environment as Air. Select Objects as Glass.

4. Set the laser to any arbitrary angle, pointing to the square. Turn on the laser. The laser beam should come out from the back side.

5. Note (figure out how), the position of the refracted ray coming out of the glass on the other side.

6. Change the material of the Object to “Air”. This will cause the ray to go straight (since refractive indices of environment and square are the same). Note the position of this ray.

7. Measure the distance that the ray shifts when the Object is Air and when it is Glass (figure out how to do this). Enter the results in Table 6.

8. Measure the thickness of the square. Enter all data in Table F.

9. Use equation 6 to calculate the shift, and compare with your measured value.

h

d

 

(6)

 

CASE G: Deviation of light by a prism (see figure 3)

1. After opening the simulation, select “PRISM”.

2. From the bottom panel, select the Triangle (prism). Set Reflections Off. Turn on Normal.

3. Select the Environment as Air. Select Objects as Glass.

4. Set the laser to any arbitrary angle, pointing to the prism. Turn on the laser. The laser beam should come out from the other side.

5. Use the protractor to measure the angle of incidence θi , angle of refraction θr, angle of the prism A , and angle of Deviation δ, and record them in Table G.

6. Calculate the angle of deviation by using equation (4), and compare with measured value. Use the refractive index of glass found in Case C.

 

CASE H: Focal Length of a Convex Lens (see figure 4) (Part A: STANDING WAVES ON A STRING Using PhET simulation)

1. Open the simulation: Geometric Optics.

2. Select Principal Rays and Screen. Select some values of Curvature, Refractive Index and Diameter of the lens.

3. Place the lamp al some position on the principal Axis (the horizontal line passing through the center of the lens).

4. Move the screen until the image becomes a small dot. The image of the object is now in focus on the screen.

5. Select the Ruler, and measure the distance from the center of the lens to the light source. (Measure to the point where the rays join together). This is the Object distance ‘p’. Now measure the image distance ‘q’ from the lens to the screen (to the point where the rays join). You may have to select a pencil or an arrow as the object to do this.

6. Note the data in Table H, and calculate the focal length, ‘f’, of the lens.

7. Repeat for several different positions of the object. Have at least one position where you get a virtual image (i.e. when object is between lens and the focal length).

8. Measure the focal length (this is the distance from lens to the ‘X’ on the Principal Axis.

RESULTS

All values are measured values unless mentioned. Attach at least one image of each case with your report.

 

TABLE A: LAW OF REFLECTION

Trial number Angle of Incidence Angle of Reflection Percent Difference

 

TABLE B: LAW OF REFRACTION (Part A: STANDING WAVES ON A STRING Using PhET simulation)

Material Trial number Angle of Incidence Angle of Refraction Refractive Index (equation 1) Average of three values Percent Error in refractive index
Water
Water
Water
Glass
Glass
Glass
Mystery A
Mystery A
Mystery A

TABLE C: LAW OF REFRACTION AGAIN

Material Trial number Angle of Incidence Angle of Refraction Refractive Index (equation 1) Average of three values Percent Error in refractive index
Glass
Glass
Glass
Mystery B
Mystery B
Mystery B

TABLE D: TOTAL INTERNAL REFLECTION

 

Material Trial number Angle of Incidence Angle of Refraction Critical Angle

Calculated

 Percent Error in Critical Angle
Water-Air
Glass-Air

 

 

 

TABLE E: TOTAL INTERNAL REFLECTION AGAIN

 

Material Trial number Angle of Incidence Angle of Refraction Critical Angle

Calculated

 Percent Error in Critical Angle
Water-Air
Mystery-Air

 

 

TABLE F: REFRACTION LIGHT RAY SHIFT

Trial Number Angle of Incidence Angle of Refraction Thickness ‘h’ of the square Measured Value of Shift in the Ray Calculated Value of the Shift Percent error in shift

 

TABLE G: DEVIATION OF LIGTH FROM A PRISM

Trial Number Angle of Incidence Angle of Refraction Angle of Prism Angle of Deviation Calculated Angle of Deviation Percent error in angle of Deviation
No Distance from Lens to Object

p

 Distance from Lens to Image

q

 Calculated Focal Length by equation 1

f
Average value of Focal Length
Percent error

TABLE H: FOCAL LENGTH OF A CONVEX LENS (Part A: STANDING WAVES ON A STRING Using PhET simulation)

 
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