Exam 4.0 COMPREHENSIVE EXAM 10 December 2003 General Physics I (PHSX 2010) Adam Johnston

REMOVE THIS COVER SHEET ONLY WHEN TOLD TO DO SO. MAKE SURE TO PUT YOUR NAME AND SEAT NUMBER ON THE FIRST PAGE OF THE EXAM BEFORE YOU TURN IT IN. YOU MAY KEEP THIS COVER SHEET, TURN IT IN WITH YOUR TEST, OR RECYCLE IT.

When, in disgrace with fortune and men's eyes, I all alone beweep my outcast state, And trouble deaf heaven with my bootless cries, And look upon myself, and curse my fate, Wishing me like to one more rich in hope, Featured like him, like him with friends possessed, Desiring this man's art and that man's scope, With what I most enjoy contented least; Yet in these thoughts myself almost despising, Haply I think on thee—and then my state, Like to the lark at break of day arising From sullen earth, sings hymns at heaven's gate; For thy sweet love rememb'red such wealth brings That then I scorn to change my state with kings.

W. Shakespeare

|g| = 9.80 m/s2

Patm=1.013 × 105 Pa R = ⋅8 3145. J / (mol K)

NA = 6.022 × 1023 mol-1 cwater = 4186 J/ (kg °C) cice = 2090 J/(kg °C) cair = 721 J/(kg °C)

Lf, water = 334000 J/kg

Lv, water = 2256000 J/kg k J K= × −1 38 10 23. /

FrrF

mgwNfmaFa

acbbx

tavv

xxavv

tatvxx

net

xx

xx

x

x

x

x

⊥==

===

−±−=

+=

−+=

++=

τθτ

µ

sin

24

)(2

2

0

020

2

221

00

W Fd= cosθ

KE mv= 12

2 GPE mgh=

P

Wt

Fvavg= =

v vFt p= ∆ v vp mv=

F Gm m

rgrav. = 1 22

G = 6.673 × 10-11 N m2/kg2

a

vr

rc = =2

2ω

ω =vr

τ αnet I=

I mrpoint = 2

I mrdisk = 12

2

L I= ω

Rot KE I. = 1

22ω

ρ =mV

PFA

=

F gVB = ρ P gh= ρ

F = Av

P gh v+ + =ρ ρ12

2 constant

T TK C= + 27315.

PV nRT NkT= =

KE mv kT= =12

2 32rms

Q cm T= ∆ Q mL=

∆U Q W= − e W Q Q Q= = −/ /H C H1

Q W QH C= +

W P V= ∆

? S = Q/T

Adiabatic = “Q = 0 ”

Isothermal = “Constant temperature” Isochoric = “Constant volume” Isobaric = “Constant pressure”

PE kx= 1

22

r rF kx= −

fT

=1

2m

Tk

π=

2L

Tg

π=

v fw = λ

fnv

Lnw=

2 , n = 1, 2, 3 . . .

fnv

Lnw=

4 , n = 1, 3, 5 . . .

f fv vv vobs sw obs

w s=

±∓

Advice/Info: Celebrate your knowledge of physics! Show your work clearly for full credit. Ask questions if you have them. Check your answers, paying careful attention to significant figures and units of measurement. (All numeric values are good to 3 significant figures.) Be calm and confident. Don’t look at your neighbor’s answers – he’s just as lost as you are. For the love of all things beautiful, and for the sake of your grade, please circle your answers. Take a deep breath. Ignore air resistance on this exam. Have a great break. You should have five (5) pages in this exam, not including the cover sheet. 150 points are possible.

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Exam 4.00 NAME: ____________________________________ SEAT NUMBER:_____ 10 December 2003 General Physics I (PHSX 2010) SCORE: / 150 Adam Johnston

Multiple choice: Each question is worth 5 points, for a grand total of 60 points in this section. 1. The following is a graph of position versus time for a mass oscillating on a spring. Clearly circle one point on the

graph for which the kinetic energy is a maximum.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

time

po

siti

on

2. Dr. Carroll lives in a one-room shack (perfectly insulated, with no doors and no windows) in the middle of the desert.

His only appliance in the shack is a refrigerator, which runs on the mechanical energy that Dr. Carroll gives it by turning a crank. If he makes the refrigerator run while its door is wide open inside the shack, what happens? (Assume that Dr. Carroll’s body temperature and heat do not affect the rest of the shack.)

A. The temperature in the shack stays constant.

B. The temperature in the shack decreases.

C. The temperature in the shack increases.

E. There is no way to know the answer.

3. Which of the following is most directly related to a measurement of temperature?

A. The quantity of heat transferred from

molecules.

B. The quantity of random kinetic energy of

molecules.

C. The average momentum of molecules.

D. The quantity of phlogiston in the molecules.

4. Which of the following collisions would take fewer equations in order to solve for the final velocities? Assume that

all objects initially have a non-zero velocity.

A. An elastic collision between two objects on a frictionless surface.

B. An inelastic collision between two objects on a frictionless surface.

C. Both are equally difficult.

5. According to Newton’s and Kepler’s laws, by determining the period of a planet’s orbit around the Sun, you can

determine:

A. the mass of the Sun. B. the mass of the planet. C. both A & B. D. None of these.

6. Over time, the Moon will get farther from the Earth. As it does so, the speed at which it orbits will:

A. stay the same. B. increase. C. decrease. D. More information is needed to predict the

answer.

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7. Imagine that you are chasing your physics professor. You are running toward him at a velocity of 5.00 m/s, but he is

running away from you at a velocity of 5.00 m/s, so that you never catch up to him. However, you will torture this physicist by blowing your whistle at a frequency of 880 Hz. What frequency does your physics professor hear?

A. Exactly 880 Hz. B. A frequency that is lower than 880 Hz.

C. A frequency that is higher than 880 Hz.

D. No frequency. He never hears the sound.

E. More information is needed to answer

this question. 8. You are pulling a sled across a flat, snowy surface at a constant velocity. Which of the following can you conclude?

A. There is no net force on the sled.

B. The net force on the sled is in the direction that

it is moving.

C. The net force on the sled is pointed opposite of

the direction that it is moving.

D. More information is needed to say something

about the net force.

9. You witness your frictionless physics professor sliding up a frictionless incline with a constant slope. His acceleration

while sliding up the ramp is

A. the same as when he slides down.

B. greater than when he slides down.

C. less than when he slides down.

10. You are bobbing up and down on a spring. Which of the following will increase the frequency at which you bob?

A. By increasing the amplitude of the motion.

B. By increasing the spring constant. C. By increasing your mass.

D. Both A & B. E. Both A & C. F. Both B & C. 11. An fluid in a closed tube (such as in a brake line for your car) has a very small area piston on one end, and a large area

piston on the opposite end. This allows for

A. the forces on one piston to be the same magnitude as the force on the

opposite piston.

B. the pressure on one piston to be the same as the pressure on the

opposite piston. C. both A & B. D. None of

these.

12. A chemist knows that he weighs 600 N. While on the elevator from the fifth floor to the second floor of the science

building, he is standing on a scale. If the elevator has a constant velocity of 9.0 m/s downwards, what does the scale read?

A. Less than 600 N B. 600 N C. More than 600 N D. There is no way to

know.

YOU’RE DOING GREAT! KEEP GOING!

[Distracting and irrelevant thought for the day: 67 billion (give or take a few) neutrinos pass through every square centimeter of your body every second of every day (and night!). They all come from the Sun, and they don’t even tickle – not even a little bit. They tell us a little bit about how energy in the Sun is produced, something about how long things have been around, and something about particle physics. You’ll learn more about all of this next semester.]

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Situation I – Roller coaster physics: Imagine that instead of taking this wretched and painful exam, you are on a frictionless roller coaster! The roller coaster ride consists of starting from rest at some great height (point A), descending to a loop, going around the top of the loop (point B), completing the loop, and then racing towards the edge of a cliff (point C). A. [10 points] What is your speed while at the top of the loop (point B), given that you started from rest at point A? (Use the dimensions given in the diagram.)

B. [10 points] If you were sitting on a scale, what would the scale read while you were upside-down at the top of the loop (at point B)?

C. [10 points] If the cliff (point C) is 30.0 m above the ground (where you will land safely), how far from the cliff (in the horizontal direction) will you land?

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Situation II – Musical tubes : An elf-physicist (as shown at right) is blowing air across one end of a U-shaped tube with water in it. As a result of this, the water in one side of the tube rises while the water in the other side of the tube drops, so that there is a difference in height between the two water levels, labeled h. In addition, there is a column of air in between the topmost water level and the tube opening that the elf is blowing across, forming a closed-tube of length, L.

A. [10 points] What is the height difference of water, h, if the speed of the air being blown by the elf-physicist is v = 120 m/s? The density of water is 1000 kg/m3, and the density of air is 1.29 kg/m3.

B. [10 points] If there were a standing wave pattern set up in the air in the closed-tube, calculate the most fundamental frequency that would be supported within that length. Assume that the speed of sound in air is 340 m/s, L = 10.0 cm, and that an antinode of any standing wave is positioned exactly at the open end of the tube.

C.[10 points] Imagine that you want to put an end to the elf-physicist’s music, so you are going to boil all of the water in his tube! You have a 1000 Watt heater, and there is 1.00 kg of water at an original temperature of 10.0°C. What amount of time is required to raise the temperature and boil away all of this water? (If you’re looking for any constants, they are on the cover sheet of this exam.)

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Situation III – Fun with felines: All of the following questions are about a magical, frictionless cat named Oskar.

A. [10 points] You save Oskar the frictionless cat (m=8.50 kg) is kept from sliding down a ramp by holding on to his tail, as shown. What is the minimum amount of force required to keep Oskar from sliding?

B. [10 points] Now imagine that the same frictionless cat is initially at the exact center of a merry-go-round (a spinning disk with a mass of 30.0 kg and radius of 2.00 m). The disk is init ially spinning at a rate of 1.50 revolutions per second. What will the rate of rotation be when Oskar is hanging on to the very outside of the disk?

C.[10 points] If Oskar lets go of the merry -go-round, describe the velocity that he will have. That is, describe the speed and direction that he will be moving. (To fully describe his motion, draw an overhead picture of the merry-go-round and include a sketch of the path that Oskar takes after letting go.)