PHYSICS-222

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Multiple Choice Section (Each worth 1 points – Total of 10 points) Put your answers on the first page of the exam. Do not put answers on this page. 1. A 2 µF and a 1 µF capacitor are connected in series and a potential difference is applied across the combination. The 2 µF capacitor has:

A. twice the charge of the 1 µF capacitor B. half the charge of the 1 µF capacitor C. twice the potential difference of the 1 µF capacitor D. half the potential difference of the 1 µF capacitor E. none of the above

2.  Two concentric, imaginary spherical surfaces of radius R and 2R, respectively, surround a negative

point charge –Q located at the center of the two surfaces. When compared to the electric flux through the surface of radius R, the electric flux through the surface of radius 2R is

A. . B. . C. . D. . E. .

3. The diagram shows the electric field lines due to two charged parallel metal plates. We conclude that:

A. the potential of the upper plate is positive and the lower plate is negative. B. a proton at X would experience the same force if it were placed at Y. C. a proton at X experiences a greater force than if it were placed at Z. D. a proton at X experiences less force than if it were placed at Z. E. an electron at X could have its weight balanced by the electrical force.

 

Φ2 = 14Φ1 Φ2 = 12Φ1 Φ2 =Φ1 Φ2 = 2Φ1 Φ2 = 4Φ1

Physics  222  -­‐  Prac,ce  Exam  #1

 

 

4. A particular car battery has a rating of 80 A-hr. The Ampere-hour is a unit of: A. power B. energy C. force D. charge E. none of the above 5. Capacitor 1 has twice the capacitance of capacitor 2. Both capacitors are connected in parallel to a battery and are fully charged. What is the ratio of energy storage of capacitor 1 to capacitor 2: A. 1 : 4 B. 1 : 2 C. 1 : 1 D. 2 : 1 E. 4 : 1 6. A particle with mass m and charge -q is projected with speed v0 into the region between two parallel plates as shown. The potential difference between the two plates is V and their separation is d. The change in kinetic energy of the particle as it traverses this region is: A. –qV/d B. 2qV/mv02 C. qV D. mv02/2 E. none of these 7. Two small charged objects attract each other with a force F when separated by a distance d. If the charge on each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2 the force becomes: A. F/16 B. F/8 C. F/4 D. F/2 E. F

Physics  222  -­‐  Prac,ce  Exam  #1

 

 

8. Five cylindrical wires are made of the same material. Their lengths and radii are wire 1: length l, radius r wire 2: length l/4, radius r/2 wire 3: length l/2, radius r/2 wire 4: length l, radius r/2 wire 5: length 5l, radius 2r

Rank the wires according to their resistances, from the least to the greatest.

A. 1, 2, 3, 4, 5 B. 5, 4, 3, 2, 1 C. 1 and 2 tie, then 5, 3, 4 D. 1, 3, 4, 2, 5 E. 1, 2, 4, 3, 5

9. When a positive charge moves along an electric field line, it moves to a position of

A. lower potential and lower potential energy. B. lower potential and higher potential energy. C. higher potential and lower potential energy. D. higher potential and higher potential energy. E. greater magnitude of the electric field.

10. Three resistors are wired together as shown in the diagram below. It is desired to have a total effective resistance between points a and b of 4.0 kΩ. What must R be in order to achieve this result?

A. R = 1.0 kΩ B. R = 2.0 kΩ C. R = 4.0 kΩ D. R = 6.0 kΩ E. R = 9.0 kΩ

 

Physics  222  -­‐  Prac,ce  Exam  #1

b

a

400 Ω

R 6.0 kΩ

 

 

Physics  222  -­‐  Prac,ce  Exam  #1     Open Response Questions (30 points) For these problems you must clearly show how you obtained your answer. A complete answer will include a diagram with labels, if appropriate. Circle your answer. Use the back if necessary. 11.) [10 pts] A particle with a charge of -3.5×10-8 C is located 5.5 cm from a second particle with a negative charge of +2.3×10-8 C. (a) [4pts] Determine the change in electrical potential energy for this two particle system, relative to the electrical potential energy when the two particles have infinite separation.

(b) [3 pts] What is the magnitude of the Electric Field that particle 1 generates at point P ?

(c) [3 pts] When particle 2 arrives at point P what is the force that particle 2 feels?

q2 is moved from infinity to position p. How much energy does that movement represent?! !

Q1=-3.5×10-8C!

q2=+2.3×10-8C!

d = 5.5cm! P!

 

 

Physics  222  -­‐  Prac,ce  Exam  #1

12. [10 pts] A hollowed out, thick, conducting sphere has inner radius a and outer radius b. a)  [1 pt] What is the volume of material that comprises the thick conducting sphere? b)  [2 pts] If a charge 5Q were placed precisely in the center of the spherical shell, what would the

area charge density of the inner spherical surface be?

c)  [2 pts] Continuing from part (b) above, what would the area charge density of the outer spherical

surface be? d)  [2 pts] Still continuing from part (b), What is the E-field at a location between radius a and b? e)  [3 pts] Plot the E-field (vertical axis) vs radial distance from the center (horizontal axis). Assume

the 5Q charge mentioned in part (b) is still present at the center of everything.

 

a   b   r

E

 

 

Physics  222  -­‐  Prac,ce  Exam  #1

13.  [5 pts] A 1-meter long wire lies along the x-axis and has a linear charge density, λ, of 5.0 µC/m that is uniform along the wire. Consider an imaginary, spherical surface with a radius of 8.0 cm placed so that the wire runs through the center of the sphere. Determine the total electric flux through the spherical surface.

Note: If this problem had asked for the E-field or something similar, you would want to discard the

sphere and consider a cylinder of length 2R (to match the sphere’s diameter). However, since it just asks for the flux, remember the full definition of what Gauss’ Law is all about:

14.  [5 pts] A parallel plate capacitor is hooked up to a battery. The distance between the plates is 5mm and the electric field between them is 800 N/C. The mass of an electron is me = 9×10-31 [kg].

a)  What is the voltage of the battery?

b)  If an electron starts at the negative plate from rest, how fast is it traveling just as it hits the positive plate?

 

c)  Suppose the distance between the plates is doubled while the battery is still hooked up. If the

electron leaves the negative plate from rest, how fast will it be going when it reaches the center of the gap (which means it went the same 5mm distance as it did in part (b)).

 
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Momentum Conservation – 100% Correct With Step By Step Calculations

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Home>Homework Answsers>Physics homework help

Momentum Conservation – 100% Correct with Step by Step Calculations

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PRACTICE:

1. If a ball is rolling at a velocity of 1.5 m/sec and has a momentum of 10.0 kg·m/sec, what is the mass of the ball?

2. What is the velocity of an object that has a mass of 2.5 kilogram and a momentum of 1,000 kg·m/sec?

3. Tiger Woods hits 45.0-gram golf ball, giving it a speed of 75.0 m/sec. What momentum has Tiger given to the golf ball?

4. A 400-kilogram cannon fires a 10-kilogram cannonball at 20 m/sec. If the cannon is on wheels, at what velocity does it move backward? (This backward motion is called recoil velocity.)

5. “Big” Al stands on a skateboard at rest and throws a 0.5-kilogram rock at a velocity of 10.0 m/sec. “Big” Al moves back at 0.05 m/sec. What is the combined mass of “Big” Al and the skateboard?

6. As the boat in which he is riding approaches a dock at 3.0 m/sec, Jasper stands up in the boat and jumps toward the dock. Jasper applies an average force of 800 Newton’s on the boat for 0.30 seconds as he jumps.

a. How much momentum does Jasper’s 80-kilogram body have as it lands on the dock?

b. What is Jasper’s speed on the dock?

7. Daryl the delivery guy gets out of his pizza delivery truck forgetting to set the parking brake. The 2,000 kilogram truck rolls down hill reaching a speed of 30 m/sec just before hitting a large oak tree. The vehicle stops 0.72 seconds after first making contact with the tree.

a. How much momentum does the truck have just before hitting the tree?

b. What is the average force applied by the tree?

8. Two billion people jump up in the air at the same time with an average velocity of 7.0 m/sec. If the mass of an average person is 60 kilograms and the mass of Earth is 5.98 × 1024 kilograms:

a. What is the total momentum of the two billion people?

b. What is the effect of their action on Earth?

9. Tammy, a lifeguard, spots a swimmer struggling in the surf and jumps from her lifeguard chair to the sand beach. She makes contact with the sand at a speed of 6.00 m/sec leaving an indentation in the sand 0.10 meters deep.

a. If Tammy’s mass is 60 kilograms, what is momentum as she first touches the sand?

b. What is the average force applied on Tammy by the sand beach?

10. When a gun is fired, the shooter describes the sensation of the gun kicking. Explain this in terms of momentum conservation.

11. What does it mean to say that momentum is conserved?

12. What is the momentum of a 100-kilogram fullback carrying a football on a play at a velocity of 3.5 m/sec?

13. What is the momentum of a 75.0-kilogram defensive back chasing the fullback at a velocity of 5.00 m/sec.?

14. A 2,000-kilogram railroad car moving at 5 m/sec to the east collides with a 6,000-kilogram railroad car moving at 3 m/sec to the west. If the cars couple together, what is their velocity after the collision?

15. A 4-kilogram ball moving at 8 m/sec to the right collides with a 1-kilogram ball at rest. After the collision, the 4-kilogram ball moves at 4.8 m/sec to the right. What is the velocity of the 1-kilogram ball?

16. A 0.0010-kg pellet is fired at a speed of 50.0m/s at a motionless 0.35-kg piece of balsa wood. When the pellet hits the wood, it sticks in the wood and they slide off together. With what speed do they slide?

17. Terry, a 70-kilogram tailback, runs through his offensive line at a speed of 7.0 m/sec. Jared, a 100-kilogram linebacker, running in the opposite direction at 6.0m/s, meets Jared head-on and “wraps him up.” What is the result of this tackle?

18. Snowboarding cautiously down a steep slope at a speed of 7.0 m/sec, Sarah, whose mass is 50 kilograms, is afraid she won’t have enough speed to travel up a slight uphill grade ahead of her. She extends her hand as her friend Trevor, having a mass of 100 kilograms is about to pass her traveling at 16 m/sec. If Trevor grabs her hand, calculate the speed at which the friends will be sliding.

19. Tex, an 85.0 kilogram rodeo bull rider is thrown from the bull after a short ride. The 520 kilogram bull chases after Tex at 13.0 m/sec. While running away at 3.00 m/sec, Tex jumps onto the back of the bull to avoid being trampled. How fast does the bull run with Tex aboard?

20. Identical twins Kate and Karen are rowing their boat on a hot Summer afternoon when they decide to go for a swim. Kate, whose mass is 45 kilograms, jumps off the front of the boat at a speed of 3.00 m/sec. Karen jumps off the back at a speed of 4.00 m/sec. If the 70-kilogram rowboat is moving at 1.00m/s when the girls jump, what is the speed of the rowboat after the girls jump?

21. A 0.10-kilogram piece of modeling clay is tossed at a motionless 0.10-kilogram block of wood and sticks. The block slides across a frictionless table at 15 m/sec.

a. At what speed was the clay tossed?

b. The clay is replaced with a “bouncy” ball tossed with the same speed. The bouncy ball rebounds from the wooden block at a speed of 10 meters per second. What effect does this have on the wooden block?

Why?

22. A net force of 100 Newton’s is applied to a 20-kilogram cart that is already moving at 3 meter per second. The final speed of the cart was 8 meters per second. For how long was the force applied?

23. A 3-kilogram ball is accelerated from rest to a speed of 10 m/sec.

a. What is the ball’s change in momentum?

b. What is the impulse?

c. If a constant force of 40 Newton’s is applied to change the momentum in this situation, for how long does the force act?

24. A 2,000-kilogram car uses a braking force of 12,000 Newton’s to stop in 5 seconds.

a. What impulse acts on the car?

b. What is the change in momentum of the car?

c. What is the initial speed of the car?

25. A 60-kilogram high jumper lands on a mat after her jump. The mat brings her to a stop after 1 second. She was traveling at 5.0 m/sec when she landed on the mat. Note: The speed of the jumper at the top of her jump, before she started to fall toward the mat, was 0 m/sec.

a. What is the change in momentum for the jumper?

b. What is the force felt by the jumper upon impact with the mat?

26. A 0.5-kilogram soccer ball is kicked with a force of 50 Newton’s for 0.2 seconds. The ball was at rest before the kick. What is the speed of the soccer ball after the kick?

27. A baseball player hits a 0.155-kilogram fastball traveling at 44.0 m/sec into center field at a speed of 50.0 m/sec. If the impact lasts for 0.00450 second, with what force does he hit the baseball?

28. Tom Sawyer launches his 180-kilogram raft on the Mississippi River by pushing on it with a force of 75 Newton’s. How long must Tom push on the raft to accelerate it to a speed of 2.0 m/sec?

29. In terms of impulse, why is the ride much more comfortable when an airplane is flying at constant speed versus when it is taking off or landing?

30.  The weatherman tells you that today will reach a high of 45°F. Your friend from Sweden asks what the temperature will be in degrees Celsius. What value would you report to your friend?

31.  Your father orders a fancy oven from England. When it arrives, you notice that the temperature dial is calibrated in degrees Celsius. You wish to bake a cake at 350°F. At what temperature will you have to set the dial on this new oven?

32.  Your new German automobile’s engine temperature gauge reads in Celsius, not Fahrenheit. You know that the engine temperature should not rise above about 225°F. What is the corresponding Celsius temperature on your new car’s gauge?

33.  Your grandmother in Ireland sends you her favorite cookie recipe. Her instructions say to bake the cookies at 190.5°C. To what Fahrenheit temperature would you set the oven to bake the cookies?

34.   A scientist wishes to generate a chemical reaction in his laboratory. The temperature values in his laboratory manual are given in degrees Celsius. However, his lab thermometers are calibrated in degrees Fahrenheit. If he needs to heat his reactants to 232°C, what temperature will he need to monitor on his lab thermometers?

35.  You phone a friend who lives in Denmark and tell him that the temperature today only rose as high as 15°F. He replies that you must have enjoyed the warm weather. Explain his answer using your knowledge of the Fahrenheit and Celsius scales and conversion formulas.

36.  A gas has a boiling point of -175°C. At what Kelvin temperature would this gas boil?

37.  A chemist notices some silvery liquid on the floor in her lab. She wonders if someone accidentally broke a mercury thermometer, but did not thoroughly clean up the mess. She decides to find out of the silver stuff is really mercury. From her tests with the substance, she finds out that the melting point for the liquid is 275 K. A reference book says that the melting point for mercury is -38.87°C. Is this substance mercury? Explain your answer and show all relevant calculations.

38.  You are at a Science Camp in Florida. It’s August 1st. Today’s activity is an outdoor science quiz. The first question on the quiz involves a thermometer that reports the current temperature as 90°. You need to state the temperature scale in which this thermometer is calibrated: Kelvin, Fahrenheit, or Celsius. Which scale is correct? Defend your answer with your knowledge of the temperature scales.

 

 
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Physics – Homework 1 (Need Detailed Steps With 100% Correct Answers)

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Name: Lab Day/Time:

Homework 1 Electrostatics

Homework is due at the beginning of the Wednesday lecture. It must be handwritten, not typeset. The multiple- choice answers must be circled. In the space after the problem, a short justification of each multiple-choice the answer must be included. The open-response answers must be worked out clearly using good physics presentation and will be graded on correctness and how carefully the work is explained. The problems should be worked in the space after the problem on the assignment printout; additional paper may be used if needed. No credit will be given for answers without appropriate supporting work. Minimum good presentation requires the following: (1) Symbolic expression for any formula, (2) Manipulation of symbolic expressions, not numeric expressions, (3) Substitution of numbers with units, (4) Reporting final answers with correct units and vector expressions, (5) Enough English description to allow the reader to have some idea what you are doing without looking at the math.

Early Questions

The questions in this section are over material that will be covered by Friday. These may be worked before the other questions.

Homework Problem 1.1 A 10cm sphere charged with a car battery (12V), picks up a positive charge of +100pC. How many excess or deficient electrons are on the sphere?

Select One of the Following:

(a) 3.2 × 109 deficient electrons

(b) 1.1 × 1014 excess electrons

(c) 6.7 × 1011 deficient electrons

(d) 9.5 × 105 excess electrons

(e) 6.3 × 108 deficient electrons

Homework Problem 1.2 Your standard number 2 mechanical pencil has a graphite lead with mass 0.05g. How many protons are in this quantity of graphite? The atomic mass of carbon is 12g/mole and the atomic number is 6.

Select One of the Following:

(a) 3.1 × 1010protons

(b) 1.5 × 1022protons

(c) 5.1 × 1024protons

(d) 2.3 × 1021protons

(e) 6.5 × 1023protons

1

 

 

Homework Problem 1.3 An insulating cylinder has height 5cm and radius 10cm. If it carries a uniform surface charge density σ = −1µC/m2 including the ends, compute the total charge of the cylinder.

Select One of the Following:

(a) Q = −2 × 10−2C

(b) Q = −3 × 10−4C

(c) Q = −5 × 10−6C

(d) Q = −9 × 10−8C

Homework Problem 1.4 A problem you should have easily been able to do in Phys 111, but I get asked it all the time when I ask for a good question on electricity and magnetism the first day of class. Suppose a human can confortably live in a spaceship accelerating at 1g = 9.81 m

s2 , ignoring relativistic effects, how long does it take

the spaceship to reach the speed of light? Report your answer in years. You may use the approximate conversion 1yr = π × 107s.

Select One of the Following:

(a) 15.7yr

(b) 0.19yr

(c) 0.97yr

(d) 15, 000yr

Homework Problem 1.5 How does the mass of the electron compare with the mass of the proton?

Select One of the Following:

(a) The two masses are equal.

(b) The electron is slightly more massive than the proton.

(c) The electron is slightly less massive than the proton.

(d) The electron is greatly more massive than the proton.

(e) The electron is greatly less massive than the proton.

2

 

 

Homework Problem 1.6 In the nuclear process “beta decay”, a neutron is converted into some other charged particles, one of which is a proton. Some neutral particles are also emitted. What other charged particle must be emitted in beta decay?

Select One of the Following:

(a) an electron or something with the charge of an electron

(b) two electrons or particles with total charge equal to two electrons

(c) a proton or something with the charge of a proton

(d) an electron and a proton

(e) No other charged particles are required.

Multiple-Choice Questions

The questions in this section are over material that will be covered by the Monday before the assignment is due.

Homework Problem 1.7 A patch of positive charge is placed on a conducting sphere. Where will the positive charge be at a later time? Assume no charge is lost to the environment.

Select One of the Following:

(a) The charge will remain in the same place.

(b) The charge will stay bunched together but will move around the surface of the conductor.

(c) The charge will separate as much as possible spreading over the surface of the conductor.

(d) The charge will transform into neutral charge and disappear.

(e) The charge will spread apart, but will eventually come back together.

3

 

 

Homework Problem 1.8 Which of the following describes an experiment that demonstrates that there are at least two different types of electric charge?

Select One of the Following:

(a) Rub one pair of rods made of the same material – for example, glass – with felt. Observe that the glass rods repel one another.

(b) Charge a pair each of glass and rubber rods by rubbing them with felt. Observe that that (1) the glass rods repel each other, (2) the glass rods attract the rubber rods, and (3) the rubber rods repel each other.

(c) Charge a pair each of glass and quartz rods by rubbing them with felt. Observe that that (1) the glass rods repel each other, (2) the quartz rods repel the glass rods, and (3) the quartz rods repel each other.

Homework Problem 1.9 Can a charged object exert a force on an uncharged insulator? If yes, why; if no, why not?

Select One of the Following:

(a) Yes, by inducing an electrical polarization in the insulator; the insulator is then attracted to the charged object.

(b) Yes, by inducing an electrical polarization in the insulator; the insulator is then repelled by the charged object.

(c) No, because uncharged objects do not feel electrical forces.

(d) No, because only conductors are attracted to or repelled by charged objects.

(e) No, because an insulator does not permit the motion of electric charge.

Homework Problem 1.10 It used to be that one could count on a water pipe as a good “ground”. A “ground” is a continuous conducting path to a long conductor buried in the Earth. Today, plumbing often involves plastic pipes and valves. Explain why this makes a water pipe something we now have to be careful of as a ground.

Select One of the Following:

(a) Plastic is only a conductor part of the time.

(b) The plastic is an insulator and may prevent there from being a continuous path to ground.

(c) Water pipes do not go into the ground anymore and thus won’t be grounded.

(d) The plastic will prevent the water from absorbing the charge.

(e) The plastic will divert any charge going to ground into the water which will shock anyone who uses the water.

4

 

 

Homework Problem 1.11 Which of the following describes an experiment that demonstrates that there are at least two different types of electric charge?

Select One of the Following:

(a) Rub one pair of rods made of the same material – for example, glass – with felt. Observe that the glass rods repel one another.

(b) Charge a pair each of glass and rubber rods by rubbing them with felt. Observe that that (1) the glass rods repel each other, (2) the glass rods attract the rubber rods, and (3) the rubber rods repel each other.

(c) Charge a pair each of glass and quartz rods by rubbing them with felt. Observe that that (1) the glass rods repel each other, (2) the quartz rods repel the glass rods, and (3) the quartz rods repel each other.

Homework Problem 1.12 After sliding down a plastic slide at the park, your hair stands on end. It continues standing on end even after you get off the slide. What does this imply?

Select One of the Following:

(a) It implies that you have picked up a net charge from the slide.

(b) It implies that your hair has become polarized.

(c) It implies that your hair is covered in water and has become a better conductor.

(d) It implies that your hair has become conducting.

(e) It implies that your hair has become insulating.

Homework Problem 1.13 When an object is grounded, its net charge is reduced to approximately zero. Is this consistent with the Law of Conservation of Charge, if so how?

Select One of the Following:

(a) It is not consistent with conservation of charge; charge is actually destroyed when an object is grounded. Conservation of Charge only applies in some cases.

(b) It is consistent with Conservation of Charge; charge is actually destroyed on the object, but an equivalent charge will be created somewhere else in the universe.

(c) It is consistent with Conservation of Charge; charge is not destroyed but is transferred to another object.

5

 

 

Homework Problem 1.14 A negatively charged golf tube (plastic rod) is brought near an uncharged conducting bucket. A positively charged pith ball is suspended within the bucket. Select the figure that accurately shows how the pith ball will react.

Select One of the Following:

(a) Figure (a) (b) Figure (b) (c) Figure (c)

GT

conductor

+

_ _

pith

Figure (a)

GT

conductor

+

_ _

pith

Figure (b)

GT

conductor

+

_ _

pith

Figure (c)

6

 

 

Open Response Questions

All questions in this section must be worked. One of the questions will be graded.

Homework Problem 1.15 A hula-hoop (a circular hoop) has radius 0.6m and linear charge density around its edge of 0.3µC/m. What is the total charge of the hoop in Coulombs?

7

 

 

Homework Problem 1.16 Since 1982, a penny has contained 2.5grams of copper. The atomic weight of copper is 63.546g/mole and the atomic number is 29. How many electrons are in a penny?

8

 

 

Homework Problem 1.17 In the following, explain each step carefully and provide a drawing. A Coke can is brought into the electric field of a negatively charged golf tube.

(a)What is the direction of the force on the Coke can and why?

(b)The Coke can is then grounded in the presence of the golf tube. The golf tube had negative charge then what is the sign of the charge on the Coke can?

(c)What is the direction of the force on the Coke can after grounding and why?

9

 
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Physics Report

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Title of the Report

A. Partner, B. Partner, and C. Partner

Abstract

The report abstract is a short summary of the report. It is usually one paragraph (100-200 words) and should include about one or two sentences on each of the following main points:

1. Purpose of the experiment 2. Key results 3. Major points of discussion 4. Main conclusions

Tip: It may be helpful if you complete the other sections of the report before writing the abstract. You can basically draw these four main points from them.

example: In this experiment a very important physical effect was studied by measuring the dependence of a quantity V of the quantity X for two different sample temperatures. The experimental measurements confirmed the quadratic dependence V = kX2 predicted by Someone’s first law. The value of the mystery parameter k = 15.4 ± 0.5 s was extracted from the fit. This value is not consistent with the theoretically predicted ktheory = 17.34 s. This discrepancy is attributed to low efficiency of the V -detector.

1. Introduction

This section is also often referred to as the purpose or plan. It includes two main categories:

Purpose: It usually is expressed in one or two sen- tences that include the main method used for accomplish- ing the purpose of the experiment.

Ex: The purpose of the experiment was to determine the mass of an ion using the mass spectrometer.

Background and theory: related to the experiment. This includes explanations of theories, methods or equa- tions used, etc.; for the example above, you might want to explain the theory behind mass spectrometer and a short description about the process and setup you used in the experiment. It is important to remember that report needs to be as straightforward as possible. You should comprise only as much information as needed for the reader to un- derstand the purpose and methods. Your should also pro-

vide additional information such as a hypothesis (what is expected to happen in the experiment based on the theory) or safety information. The main focus of the introduction mainly focuses on supporting the reader to understand the purpose, methods, and reasons for these particular meth- ods.Purpose of the experiment

Example:

Calculation of the pressure coefficient Cp

From the lectures notes, Cp can be obtained by the eq. (1)

−Cp = P −P∞

1 2 ∗ρ∗U

2 ∞

(1)

Where P and P∞ are respectively the local pressure and the atmosphere pressure far away. U∞ is the wind velocity

Preprint submitted to supervisor April 16, 2020

 

 

of the wind tunnel.

Calculation of the lift coefficient CL

First, the expression for the pressure force acting nor- mal to the chord line is given in the lecture notes as eq.(2),

Cn = ∮ Cp(−n̂∗ ŷ)dl, (2)

with Cp the coefficient of lift and n̂ the unit normal vector pointing out of the surface, ŷ is the unit vector in the direction normal to the chord line. dl is the length of an infinitesimal line element. Similarly, the axial component can be express as eq.(3)

Ca = ∮ Cp(−n̂∗ x̂)dl, (3)

2. Method

This is a short (half a page or so) passage in your report which should include the experimental process exactly as it was done in the laboratory. The procedure should be written in paragraph form. You should not copy the lab manual. It is possible that the experiment you have done has slightly difference procedures than in the manual. You should not include any results (things happened during the procedure). A good rule of thumb for complete but brief experimental procedures is to provide enough information so that the reader of your report would be able to repeat the experiment.

A first offset measurement was taken with the pressure scanner, sample at 800 Hz for 10 seconds , while matlab was taking an offset measurement. After the offset measur- ment done , the wind tunnel VFD RPM was set to reach the target U∞ within ±0.5m/s. For each of the following α= [-8 -6 -4 -2 0 2 4 6 7 8 9 10 11 12 13 14 16 18], the same procedure was repeated :

The turntable was set to the right angle of attack (as shown in fig.(1)). Then the dynamic pressure and the tem- perature were taken (1000 Hz for 30 seconds for pressure, and 14 Hz for 10 seconds for the temperature).

While Matlab was taking the data , the pressure scan- ner was run to take measurement at 800 Hz for 60 seconds. After changing the angle, a break of 5 seconds was taken in order to fully settle the flow into a steady state before taking the next set of measurements.

The post-experiment calculations were realized with Matlab. First, the pressure offset was computed in order to get the right pressure measurement. With the 2 off- set measurements and the getfiledate.m Matlab code, the time of each offset has been taken. A linear interpolation was realized to get the offset at any time.

The pressure points were linked to the corresponding measurement value of the scanner and the time of each measurement was obtained with the getfiledate.m code. The new pressure were finally taken by subtraction of each corresponding time offset to the measurement pressure for every angle of attack.

The lower and upper Cp values were computed with eq.(1). The denominator in the eq.(1) (P − P∞) corre- spond to the new pressure calculated by subtraction of the offset . As the pressure points does not surround the airfoil entirely, the Cp curves had to be closed by interpo- lation of the data points using piecewises cubic Hermite polynomials (PCHIP) for the last three points to estimate a value for the trailing edge. An example of a Cp curve for a certain angle of attack is shown in fig.(5).

Next, the CL values for each angle of attack were com- puted using eq.(6). The coordinate system used in eq.(6) is shown in fig.(2). fig.(5) shows the resulting plot of this calculation.

Finally, the errors in the lift coefficient were computed using eq.(9). The different variance values were given in the lab document and calculated using eq.(8). fig.(3) shows the resulting plot of this calculation.

Figure 1: Set up of the airfoil experiment

2

 

 

3. Results

In this section all the results of the experiment is re- ported, including:

Raw data- in forms of graphs or tables. Each graph, table, or figure should be labeled and titled properly. Mak- ing tables and figures is helpful when you refer to and explain each of them in the report. Make sure that you attach the appropriate units to all physical quantities.

Assume that the reader has not done the lab; so give clear definition of each symbol that is used in the re- port. (ex: âĂIJL is the length of the pendulumâĂİ.)

Important results âĂŞ It is expected to use complete sentences to communicate the main results, which also should be expended to discussion section. (Ex: âĂIJThe gravitational acceleration was calculated to be 9.98 m/sâĂİ) This enables the important results to stand out from all the calculations, tables, and figures.

Calculations Normally, one sample of each calcula- tion is necessary. For example, if the speed of an object is calculated for 6 trials, you are expected to write out calcu- lations for only one of them. However, it is important to mention that the calculation was repeated 6 times and give the average of all 6. Significant figures should be consid- ered in all calculations (see appendix of âĂIJSignificant Figure RulesâĂİ as a resource with significant figures). Again, make sure units are included in all calculations.

Example: The resulting slope of the Cl for α ∈ [−8, 8] is 6.174 rad and 6.209 rad for α ∈ [−4, 4] . This devi- ates by 0.1090 and 0.0745 respectively from the 2π value predicted by thin airfoil theory, indicating larger errors for higher AoA’s.

The max theoretical error ∆Cl was calculated to be 0.0887, and occurred at α = 16◦, which is in the stall re- gion. Outside of the stall region the max error was calcu- lated to be 0.0391, at α = 8◦

The standard deviations presented in tab.1 were used in the result above. σqinf , and σPi were found with eqn (8). However, σPi is a vector for all of the pressure ports, and will not be presented.

Figure 2: Resulting plot of ∆CL

Table 1: Value of variance σP0 σα σqinf 3.000 0.250 0.453 [Pa] [deg] [Pa]

Figure 3: Resulting plot of CL compared to experimental data

Figure 4: – Cp for α = 8◦

4. Discussion

The most important part of your report is the discus- sion section. Here you explain your results and allow your instructor to see that you have a thorough understanding of the scientific concept of the experiment and the results. In this section you also compare the expected (theoreti- cal) results with actual (experimental) ones. It is possible that your experiment turns out not exactly the way it was supposed to. Analyze and discuss why the results might have been different and try to explain why you obtained the results you did. Be specific what caused the error: faulty equipment, inaccurate measurements or calculation errors. After you have discussed the cause of the error,

3

 

 

try to suggest how to avoid the error and how to setup the experiment more effectively (ex: be more careful with measurements, use more precise equipment, etc.)

Example According to thin airfoil theory, the Cl curve for cambered airfoils should be straight for low angles of attack with a slope of ¡textit2π. It should also have a positive lift at α = 0◦. The resulting CL curve clearly follows this trend, albeit not perfectly, especially at higher AoA’s. This likely follows from the assumption of a thin airfoil, as the NREL S826 has a non negligible aspect ratio of 5 .

Furthermore, the boundary layer acts as a streamline, essentially adding some minute thickness to the airfoil flow. It would therefore experience a higher adverse pressure gradient due to the curvature, and thus earlier separation. This can also be observed in figure 4, where a high pressure gradient is starting to form already for α = 8◦ at x

c ≈ 0.2.

Furthermore, stall can be predicted to be about α = 12◦ from figure 3. This seems to fit well with previous experimental data shown in pink [2], . Larger theoreti- cal errors are expected in this region, as separation and irregular flow further complicates the theory.

The discrepancies are also likely to be due to the mea- surement errors described in the theory section. The max calculated error ∆CL is 5.93 % of the total CL.

5. Conclusion

This section is a short paragraph that includes one or two sentences. Conclusion summarizes the major result(s) of the experiment.

Example The goal of this lab was experimentally mea- sure pressure around an airfoil for different AoA’s and to compare the resulting lift data with theory. This was done with numerical integration of the pressure distrubution, while also adjusting for measurment errors. There seems to be good agreement between the lab data and theory. The resulting slope of the CL curve deviates at a maxi- mum 0.109 from thin airfoil theory outside the stall region. This is probably due to the thickness of the airfoil, as well as the measurement error in the equipment. As expected stall occurs at about α = 12◦, which can be qualitatively observed in both the CL and CP curves.

References

[1] Scanivalve: MPS4264 Miniature Pressure ScannerManual, http://www-cs-faculty.stanford.edu/˜uno/abcde.html

[2] Airfoil tools: Previous experimental data for the NREL S826, http://airfoiltools.com/airfoil/details?airfoil=s826-nr

4

 

  • Introduction
  • Method
  • Results
  • Discussion
  • Conclusion
 
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waves

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Waves, particles and measurement

1. Sir Isaac Newton’s corpuscular theory of light in Opticks treated light as

Select one:

a. Having a discrete mass

b. Both energy and matter

c. A stream of particles

d. Eternal

 

2. Plato thought of light as coming from

Select one:

a. The sun

b. The air

c. Our eyes

d. The gods

 

3. The appearance of waves spreading out after moving through an opening is one example of the phenomenon called

Select one:

a. Corpuscular theory

b. Huygens pattern

c. Diffraction

d. Maxwell’s Law

 

4. Which of the following is a practical example of destructive interference

Select one:

a. LCD displays

b. Window blinds

c. Sound cancelling headphones

d. Polarized sunglasses

 

5. Light is

Select one:

a. Only a Wave

b. Only a Particle

c. Both a wave and a particle

d. Neither a wave nor a particle

6. Quantum physics can best be described as

Select one:

a. The study of turbulent compressible fluid motions

b. The study of matter on discrete, very small scales

c. The study of distant quasi-stellar objects in the early universe

d. The study of fission and fusion

 

7. The creation of an interference pattern is indicative of

Select one:

a. Organized molecular blockage

b. Misaligned polarization

c. Opposite charged magnetic poles

d. Wave propagation

 

8. Albert Einstein called light ______ for which he won the Nobel Prize in 1921 Lasers

Select one:

a. Lasers

b. Waves called ‘photoelectrons’

c. Energy packets named ‘photons’

d. Masers

 

 

9. The linear distance between two successive peaks on a wave is called a _____

Select one:

a. Decibel

b. Amplitude

c. Frequency

d. Wavelength

10. Light from the most distant galaxies has been travelling for ______ before reaching our eyes.

Select one:

a. Billions of years

b. Hundreds of years

c. Millions of years

d. Thousands of years

 

11. Sarah notices that when waves from two different sides of a wave tank meet the waves seem to vanish. What is she observing?

Select one:

a. Resonance

b. Annulment

c. Disintegration

d. Destructive interference

 

12. Quantum physics describes the interaction of matter and light on _____ scales

Select one:

a. Global

b. Atomic

c. Galactic

d. Imaginary

 

 

13. Thomas Young’s work compared interference patterns in water waves with light produced by his _____

Select one:

a. Difference engine

b. Double-slit experiment

c. Stream of particles

d. Shadow masks

 

 

14. Euclid identified properties of light including moving in straight lines and laws of _____

Select one:

a. Electromagnetism

b. Radiation

c. Natural Motion

d. Reflection

 

 

15. When the double slit experiment is performed with a strong coherent source of light such as a laser we observe evidence that light behaves like a wave

Select one:

True

False

 

 

16. When peaks and toughs of two waves line up and add together this is called _____

Select one:

a. Destructive interference

b. Additive alignment

c. Constructive interference

d. Corrective alignment

 

 

17. A wave can be thought of as a _____ while a particle is a ______

Select one:

a. Individual; Group

b. Pattern; Discrete object or quantity

c. Peak; Valley or trough

d. Wavelength; Frequency

 

 

18. James Clerk Maxwell discovered that light is a type of _____ and can travel through the vacuum of space

Select one:

a. Radiant matter

b. Electromagnetic wave

c. High energy particle

d. Acoustic resonance

 

19. In much the same way that Newton is associated with laws of classical mechanics, Maxwell is

Select one:

a. Electromagnetism

b. Astrophysics

c. Quantum mechanics

d. Linear algebra

 

20. The work of _____ on light was not widely regarded at the time because it was the opposite of what Newton (who was already wildly famous) had proposed

Select one:

a. Albert Einstein

b. Thomas Young

c. Aristotle

d. Christiaan Huygens

 

21.

We see water waves readily in the sea, lakes or even puddles. How do we most commonly sense waves in air?

Select one:

a. Touch

b. Sight

c. Hear

d. Taste

 

 

22. If light is seen to diffract through an opening then light behaves like

Select one:

a. A wave

b. A stream of particles

c. A single particle

d. A photon

 
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Physics Problems

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An infinitely long single wire with current I1 = 2.5 A and a rectangle wire loop with current I2 = 0.25 A are in the same plane as shown. The dimensions of the loop are a = 0.025 m and b = 0.025 m. The infinite wire is parallel to side AD of the loop and at a distance d = 0.025 m from it.
https://www.theexpertta.com/images/ytnq43wp.3ve.PNG
Randomized Variables
I1 = 2.5 A
I2 = 0.25 A
a = 0.025 m
b = 0.025 m
d = 0.025 m
Part (a) Express the magnitude of the magnetic force Fad, from I1 on wire AD in terms of I1, I2, d and the loop dimensions.
Part (b) Calculate the numerical value of Fad in N.
Part (c) Express the magnitude of the magnetic force Fbc, from I1 on wire BC in terms of I1, I2, a, b, and d.
Part (d) Calculate the numerical value of Fbc in N.
Part (e) Is the force of Fad repulsive or attractive?
Part (f) Is the force of Fbc repulsive or attractive?
Part (g) The forces of Fad and Fbc both act on the infinite wire I1. Do they sum to produce a net attractive or repulsive force?
Part (h) Calculate the numerical value of the sum of the forces F = Fab – Fbc on the infinite wire in N.
2nd question:
A solenoid is created by wrapping a L = 90 m long wire around a hollow tube of diameter D = 4.5 cm. The wire diameter is d = 0.9 mm. The solenoid wire is then connected to a power supply so that a current of I = 9 A flows through the wire.
Randomized Variables
L = 90 m
D = 4.5 cm
d = 0.9 mm
I = 9 A
Part (a) Write an expression for the number of turns, N, in the solenoid. You do not need to take into accountthe diameter of the wire in this calculation.
Part (b) Calculate the number of turns, N, in the solenoid.
Part (c) Write an expression for the length of the solenoid (L2) in terms of the diameter of the hollow tube D, assuming it is constructed by using only 1 layer of loops (note that most solenoids are actually constructed with many layers, to maximize the magnetic field density).
Part (d) Calculate the length of the solenoid (L2) in meters.
Part (e) Calculate the magnitude of the magnetic field at the center of the solenoid in Teslas.

 
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Physic Lab

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Lab AC circuits [footnoteRef:1] [1: Adapted from https://phet.colorado.edu/en/contributions/view/5011, RLC circuits by Eric Roebuck]

Use the following PhET simulation to complete the experiment. Include this document, figures in your submission.

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

Lab Goals:

To find the frequency of resonance of a RLC series circuit.

To study the phase shift between two signals.

To investigate power in AC circuits.

Part 1 – RLC Circuit

1. Create a circuit with an AC Voltage (source) in series with a resistor, inductor, and capacitor.

2. Right click the AC Voltage and click Change Voltage and note the current value of the voltage. Click Change Frequency and note the current value of frequency.

3. Place Voltage Chart around each element in the circuit, include the AC Voltage. Make sure the polarity is consistent. Take a screen shot an insert here.

 

 

 

 

4. Mark the maximum/minimum voltage on each graph. Qualitatively note the similarities and differences between the graphs. Which graphs are in phase with one another? Which graphs are not? What about the sign of the amplitude? You can easily do that by pressing the stop button.

5. Using the RMS voltages (VRMS = V0 / √2) show that the RMS voltage on the AC Voltage is consistent with the voltage sum of each element VRMS = √ [ (VRMS,R)^2 + (VRMS,L -VRMS,C)^2 ].

6. Using the resistance, capacitance, inductance, and the frequency of the AC Voltage calculate the impedance Z. By right clicking on each element you can find the values for each component. You don’t have to change the current values but if you click on change value it will display its magnitude.

7. Place a Current Chart after the battery in the circuit. Note the maximum value of the current. Using the RMS current show that the RMS voltage from the AC Voltage is consistent with the RMS current and impedance.

 

8. Change the frequency of the AC Voltage to the resonant frequency and click Reset Dynamics. Allow the simulation to run for at least one minute to adjust. Repeat steps #4-7. What similarities and differences do you see between the two tests. Screen grab your circuit and include the picture in your lab report. Save the circuit for your own records.

Part 2 – Average Power

1. Create an RLC circuit with resonant frequency of your own choosing. Initially set the resistance to 10 Ω. For at least 7 values of frequency fill out the table below. Make sure you have at least three points above, below, and including the resonant frequency. Note IRMS and VRMS are the values leaving the AC Voltage. Refer to your lecture notes on how to calculate average power.

R=10 [Ω]

f [Hz] ω [rad/s] Z [Ω] IRMS [A] VRMS [V] PAVE [W]
           
           
           
           
           
           
           
           
           
           
           

2. Using Microsoft Excel or Google Sheets make a graph of the average power (y-axis) versus ω (x-axis). Make sure the graph has axes labeled with units included. Save a copy of the graph and include it in your submission.

3. Repeat #1-2 now with R=100 Ω and the circuit otherwise unchanged. Save a copy of the graph and include it in your submission.

R=100 [Ω]

f [Hz] ω [rad/s] Z [Ω] IRMS [A] VRMS [V] PAVE [W]
           
           
           
           
           
           
           
           
           
           
           

4. Compare the two graphs qualitatively. What role does the resistance play in an RLC circuit?

5. Screen grab your circuit and include the picture in your lab report. Save the circuit for your own records.

 
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Engineering 151 Test Module 7 Through 9

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1)

A steel cable 1.25 inches in diameter and 50 ft long is to lift a 40,000 lb weight. What is the length of the cable during lifting? The modulus of elasticity of the steel is 30×106 psi.

 

2)

A large flat plate is subjected to constant amplitude uniaxial cyclic tensile and compressive stresses. Compute the critical crack length if the fatigue life must be at least 3×106 cycles. Assume the initial maximum edge surface crack length to be 1.1 mm, and a maximum tensile stress of 160 MPa. Assume m=3.0, A=1.4×10-13MPa in meter units, and Y=1.2.

3)

Using the attached figure, for a Cu-20% Wt Ag alloy, determine the phases present, their percentage amounts, and their compositions at

a. 1000 degrees Centigrade

b. 781 degrees Centigrade

c. 779 degrees Centigrade

 
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Problem Solving

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Unit II Problem Solving Worksheet

This assignment will allow you to demonstrate the following objectives:

• Illustrate the scientific method within everyday situations. o Identify the appropriate formulas necessary to solve specific scenario questions. o Calculate and analyze the acceleration and the force in various situations.

• Explain Newton’s laws of motion at work in common phenomena. o Solve problems using mass and weight. o Explore the relationship between the first and second laws. o Identify action-reaction pairs in the third law.

Instructions: Choose 8 of the 10 problems below. Show your work in detail. Answer the questions directly in this tem- plate. Before doing this, it is highly recommending that you thoroughly review the three examples in the Unit Lesson.

1. Susan pushes her dad, David, on an ice rink with a force of 30 N. She weighs 45 kg and her dad weighs 100 kg. What are the accelerations of Susan and David?

Hint: For an example of this problem being worked out click here. To view a transcript of this video, click here.

Click here for a PowerPoint version of the video. To view a transcript of this PowerPoint click here.

2. Alice holds a black belt in Taekwondo and her fist has a mass of 0.5 kg. Her fist obtains a velocity of 5 m/s in 0.1 seconds from rest. Evaluate the average net force applied to the fist.

Hint: For an example of this problem being worked out click here. To view a transcript of this video, click here.

Click here for a PowerPoint version of the video. To view a transcript of this PowerPoint click here.

3. A lunar exploration vehicle was created by a research team. It weighs 3,000 kg on the earth. It needs an accelera- tion of 10 m/s2 on the moon. In order to have the same acceleration, what will be the net force acting on the vehi- cle on the earth? To view a transcript of this video, click here (Unit II PS_3.docx). Also, click here(Unit II PS_3.pptx) to review the power point presentation.

Hint: For an example of this problem being worked out click here. To view a transcript of this video, click here.

Click here for a PowerPoint version of the video. To view a transcript of this PowerPoint click here.

 

 

Unit II Problem Solving Worksheet 4. Three people are pushing a 500 kg of box in the same direction. Applied forces are 30 N, 20 N,

and 10 N respectively. If the acceleration of the box is 0.02 m/s2, what is the magnitude of a force created by fric- tion?

 

Hint: For an example of this problem being worked out click here. To view a transcript of this video, click here.

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5. You drive a 6,000 kg boat due north, while the wind exerts a force of 600 N due south and the water exerts a re- sistive force of 1,200 N due south. The generated force by the boat’s engines is 4,200 N. Find the magnitude and direction of the boat’s acceleration.

Hint: For an example of this problem being worked out click here. To view a transcript of this video, click here.

Click here for a PowerPoint version of the video. To view a transcript of this PowerPoint click here.

6. A machine accelerates a 5 kg missile from rest to a speed of 5 km/s. The net force accelerating the missile 500,000 N. How long does it take to arrive at the speed of 5 km/s?

Hint: For an example of this problem being worked out click here. To view a transcript of this video, click here.

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7. Peter found an amazing fact in an amusement park when he tried to ride the Magic Mountain Superman. Powerful magnets accelerate a car and its riders from zero to 45 m/s in 7 seconds. Suppose the mass of the car and riders is 5,600 kg. What is the average net force exerted on the car and riders by the magnets?

Hint: For an example of this problem being worked out click here. To view a transcript of this video, click here.

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8. Two forces of 10 N and 30 N are applied to a 10 kg box. Find (1) the box’s acceleration when both forces point due east and (2) the box’s acceleration when 10 N force points due east and 30 N force points due west.

Hint: For an example of this problem being worked out click here. To view a transcript of this video, click here.

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9. When a 60 g (=0.06 kg) tennis ball is served by a newly invented machine, it accelerates from zero to 50 m/s. The ball experiences a constant acceleration due to the impact with the racket over a distance of 0.5 m. What is the net force acting on the ball? Use the formula: a= (vf2-vi2)/2d regarding the relation among acceleration a, final ve- locity vf, initial velocity vi and the traveled distance of an object d.

Hint: For an example of this problem being worked out click here. To view a transcript of this video, click here.

?

20 N

30 N

8810 N

 

 

Unit II Problem Solving Worksheet

Click here for a PowerPoint version of the video. To view a transcript of this PowerPoint click here.

10. Cole is riding a sled with initial speed of 5 m/s from west to east. The frictional force of 50 N exists due west. The mass of the sled and Cole together is 100 kg. How far does the sled go before stopping? Use the formula: a= (vf2- vi2)/2d regarding the relation among acceleration a, final velocity vf, initial velocity vi and the traveled distance of an object d.

Hint: For an example of this problem being worked out click here. To view a transcript of this video, click here.

Click here for a PowerPoint version of the video. To view a transcript of this PowerPoint click here.

 

 
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Lab Report # 9

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Temple University physics

Refraction, Reflection, and Lenses

Unperturbed light propagates in a straight line, but the direction of propagation changes abruptly when the light encounters a reflective surface; something we take for granted when we look into the mirror. Light can also change direction when passing from one medium to another; a phenomenon known as refraction. Refraction occurs because, as the light passes into a different medium, the speed at which it can propagate is altered. To understand these phenomena, we will think of the light as idealized narrow beams called rays. Modeling the light as rays is a simple but accurate way to trace light propagation through an optical system (e.g. a mirror, a magnifying glass, or a microscope).

Learning Goals for this Laboratory:

· Become familiar with ray optics terminology

· Practice drawing ray diagrams for determining image-object relationships

· Understand how air water interfaces refract light by applying Snell’s Law

· Observe total internal reflection and understand the conditions under which it occurs

· Understand how to apply the lens equation to the human eye

Part I. Reflection

1. Hold a large shiny metal spoon at arm’s length with the concave side facing you. You should see your image in the spoon.

Question 1. Is your image upright or inverted as seen in the concave side of the spoon?

2. Now flip the spoon around so that the convex side is facing you and again hold it at arm’s length and look for your image. Flip back and forth between the convex and concave sides and observe how the images are different. For your report make a data table for Part I to compare the two images, recording in each case whether the image is upright or inverted and whether the size is magnified or reduced or neither in comparison to the original object (remember you are the object).

3. It is not always easy to determine whether and image is virtual or real without using the mirror equation. Use the mirror equation to determine whether your image is real or virtual in the two cases (convex and concave). Assume the focal distance is 1 cm and estimate the object distance (your face is the object in this situation). Be sure to use the correct signs, refer to the sign conventions for mirrors if necessary.) Include the results of your calculation in your data table for Part I.

4. With the concave side facing you, observe and record what happens to your image as you move the spoon closer and closer. Be sure to note how the size of the image changes as well as whether it remains inverted or becomes upright.

5. Look for the inflection point very close to the spoon where the image flips. It may be easier to see this point if you use your finger as the object and see how its image changes as you move it closer: at some point you should see your finger reflected upright and at about normal size.

Question 2. Show that this inflection point is the focal point of the concave mirror. To do this, use the mirror equation and the magnification equation noting that a positive magnification indicates an upright image.

Part II. Refraction

1. Place a straight object such as a pencil, chopstick, or ruler, into a clear container and fill the container with water until the object is about halfway submerged. A wine glass, glass bowl, or clear flower vase work well.

2. Observe the straight object from all sides, recording your observations for the data section of your lab report. Be sure to note whether the object appears to be bent or not when you are observing it from each position.

Question 3. Why does the object appear to be straight when viewed from directly above, but bent when you move your head slightly to either side? Use Snell’s Law to support your answer. Assume the index of refraction of air is 1 and that of water is 1.33. Include sketches where helpful.

3. Kneel down and observe the water’s surface from below. From a low enough vantage point, the surface of the water is mirror-like. Can you see this total internal reflection of the light from the object?

Question 4. Why don’t you see total internal reflection on the top surface of the water? Use Snell’s law and a sample calculation to support your answer.

Part III. Lenses – The Human Eye

Lenses make use of refraction to focus or spread out light rays.. The human eye is essentially a lens (the cornea) and a screen (the retina). See the diagram below showing the parts of the eye. Though most of the refraction occurs at the cornea, the eye actually has a lens inside to fine-tune the amount of refraction in order to focus on objects at different distances, a process called accommodation. In this virtual lab, we’ll make a simple model of the eye and see how it accommodates, then we’ll look at how corrective lenses work.

Macintosh HD:usr:home:d:002:tue77829:Box Sync:Physics Folder:Teaching:texts:giancoli algebar:Giancoli7_Images_jpg:ch_25_giancoli7_jpg:25_09_Figure.jpg

1. Open the web-based simulation https://ricktu288.github.io/ray-optics/simulator/

2. Draw a lens on the workspace by clicking on the glasses menu and selecting the ideal lens. Then click and drag to make the lens a few inches long on your screen. The lens appears as a gray line and we are viewing it from the side.

3. To the left of the lens, draw a beam of parallel rays by selecting “beam” from the menu and clicking and dragging on the workspace as you did for the lens. You can reposition or resize either the ray or the lens by clicking on their center or their ends, respectively. You should now have a beam of rays passing through the lens and converging to a point like this:

Question 5. Click on the lens. Notice that you can set its focal length to be negative or positive. What is the difference between such negative and positive lenses?

4. For the data section of your report, record how the path of the rays differs between the positive lens and negative lens.

5. Let’s add a retina and see how images form on it. Reset the focal length of the lens back to +100 units; the units are arbitrary so let’s call them “mm.” Select “blocker” form the menu and draw the blocker at the focal point of our beam of light, 100 mm from the lens. The blocker represents the retina, the location where images form when the eye is properly focused. Also add a ruler so we can measure distances. Now your setup should look something like this:

Now we have the eye properly focused on a distant object represented by a beam of parallel rays. In other words, an image of the distant object is present on the retina, so the eye sees the object clearly.

Question 6. Is the image that forms on the retina of the eye a real or virtual image? How do you know?

6. Make a prediction: if the lens and retina stay fixed, where will the light from a nearby object form: on the retina just like the image of the distant object? In front of the retina (inside the eye)? Beyond the retina (outside the eye)?

7. Now test your prediction. We will use a point source to represent a nearby object because light from nearby objects is diverging steeply outward just like that from the point source. Place a point source to the left of the lens at a position 200 mm left of the lens. Where does the image form (i.e. where does the light come to focus)? To help you see where the image forms, move the blocker out of the way. Record for the data section of your report where the light from the nearby object forms in comparison to light from distant objects.

Question 7. In the situation we have modeled, the eye can focus on distant but not nearby objects? Which type of eye dysfunction is this: nearsightedness or farsightedness?

8. As mentioned above, the normal eye can focus on both near and far objects by accommodation: changing the focal length of its lens by making it more rounded in shape as seen here.

G fig 25 G fig 25

 

Accommodate your eye by clicking on the lens and changing its focal length until the light from the point source is focused on the retina.

Record this new lens focal length of the accommodated eye as well as the focal length of the relaxed, unaccommodated eye (100 mm in our model).

Question 8. What is the new focal length of the accommodated eye? How does this compare to the focal length of the relaxed, unaccommodated eye?

9. Return your eye to its relaxed state by changing the focal length to 100 mm so the distant object is in focus. Note that the light from the nearby object is focused behind the retina.

10. Make a prediction: what type of corrective lens can we place in front of the eye in order to correct the farsightedness, bringing the image of the nearby object forward from its current position behind the retina to its proper place on the retina? A positive (converging) lens? A negative (diverging lens)?

11. Test your prediction by placing a second ideal lens to act as a corrective lens 20 mm in front of the existing eye. Adjust the focal length of your corrective lens until you get the image from the point source to land on the retina (you should end up with a value slightly larger than 180). Record the focal length and type (converging or diverging) lens that corrects farsightedness.

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7/22/2020 1:24 PM

 
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