EXAM I

Phys 172H fall 2006, Purdue University

PRINT YOUR NAME: ………………………………………… Lab section:…… Do not use other paper. Write on the back of this test if needed. All problems except the last one are multiple choice and only correct answer is graded. For the last problem only you must provide the complete reasoning and solution as requested in the problem:

• Correct answer without adequate explanations or with incorrect reasoning will be counted wrong. Cross out anything you don’t want us to read.

• Make explanations complete, but brief. Do not write a lot of prose. • Include diagrams where appropriate to explain your work. • Show what goes into a calculation, not just the final number: (2 m)/(4 s)=0.5 m/s • Give standard SI units with your results • Unless specifically asked to derive a result, you may start from the formulae given

on the equation sheet • Use correct vector notation • Your work must be legible and clear

Problem 1. A child with mass 30 kg rides on a merry-go-round, traveling from location A to location C at a constant speed 1 m/s.

a) What is the direction of p!! , the change in the child’s momentum, between locations A and B? 1) 2) 3) 4) 5) 6) 7) 8) 9) b) What is the direction of p!! , the change in the child’s momentum, between locations A and C? 1) 2) 3) 4) 5) 6) 7) 8) 9) c) What is the magnitude of the change of the momentum p

!! of the child, between

locations A and C? 1) 60 m.kg/s 2) -60 m.kg/s 3) 42.4 m.kg/s 4) -42.4 m.kg/s 5) 30 m.kg/s 6) -30 m.kg/s 7) 0 m.kg/s

d) What is the change of the magnitude of the momentum p

!! , between locations A and

C? 1) 60 m.kg/s 2) -60 m.kg/s 3) 42.4 m.kg/s 4) -42.4 m.kg/s 5) 30 m.kg/s 6) -30 m.kg/s 7) 0 m.kg/s

x

y

Answers for parts a) and b):

Problem 2. Three protons travel through space at three different speeds:

Proton A: 290 m/s Proton B: 2.9e5 m/s Proton C: 2.9e8 m/s

For which proton(s) is it reasonable to use the approximation 1!" when calculating its momentum to within 1% precision?

1. A only 2. A and B 3. A and B and C 4. none of the protons

Problem 3. An object is moving in the +x direction. Which of the following statements about the net force acting on the object could be true?

A. The net force is in the +x direction B. The net force is in the –x direction C. The net force is zero

1) A only 2) B only 3) C only 4) A and B 5) B and C 6) A and C 7) A, B, and C

Problem 4. You push a book across a table. In order to keep the book moving with constant momentum, you have to keep pushing with a constant force. Which statement explains this?

1) A net force is necessary to keep an object moving. 2) To make the net force on the book zero, you must push with a force equal and opposite to the friction force on the book. 3) The force you exert must be slightly larger than the friction force.

Problem 5. a) The gravitational force exerted by a planet on one of its moons is 3×1023 N when the moon is at a particular location. If the mass of the moon were to increase three times, what would the force on the moon be?

1) 1×1023 N 2) 3×1023 N 3) 6×1023 N 4) 9×1023 N

b) The gravitational force exerted by a planet on one of its moons is 3×1023 N when the moon is at a particular location. If the distance between the moon and the planet was doubled, what would the force on the moon be?

1) 6×1023 N 2) 3×1023 N 3) 1.5×1023 N 4) 0.75×1023 N 5) 0.33×1023 N

Problem 6. Two equal positive charges and one negative charge are positioned in space as shown below:

Which arrow best indicates the direction of the net electric force on the negatively charged object? 1) 2) 3) 4) 5) 6) 7) 8) 9) Problem 7. You hold a tennis ball at rest above your head, then open your hand and release the ball, which begins to fall. (a) At this moment, which statement about the gravitational forces between the Earth and ball is correct?

1) The force on the ball by the Earth is larger than the force on the Earth by the ball. 2) The force on the Earth by the ball is larger than the force on the ball by the Earth. 3) The forces are equal in magnitude. 4) There is not enough information to determine this.

(b) The tennis ball falls for 1 second. During this time the change in the y (vertical) component of the ball’s momentum is Δpy = –0.6 kg.m/s. What is the change in the y component of the Earth’s momentum?

1) –0.6 kg m/s 2) +0.6 kg m/s 3) zero because the ball does not exert a force on the Earth 4) zero because the Earth’s momentum can’t change 5) There is not enough information to determine this.

Problem 8. A steel ball of mass m falls from a height h onto a scale calibrated in newtons. The ball rebounds repeatedly to the same height h. The scale is sluggish in its response to the intermittent hits and displays an average force Favg. (a) The average force displayed by the scale is:

1) mg/2 2) mg 3) mgh 4) None of the above

(b) What would be average force displayed by the scale, if after every bounce the ball would rebound to somewhat lower height than in the previous bounce?

1) The same as in part (a) 2) Smaller than in part (a) 3) Larger than in part (a) 4) Not enough information to select the answer

Problem 9. SLAC, the Stanford Linear Accelerator Center, accelerates electrons through a vacuum tube two miles long. Electrons that are initially at rest are subjected to a constant continuous force of 2×10-12 N along the entire length of two miles (1 mile = 1609 m). a) Calculate the momentum of the electron moving at speed 0.01c (c is speed of light)

1) 2.7×10-24 m/s 2) 2.7×10-21 m/s 3) 3.7×10-25 m/s 4) 4.9×10-23 m/s

b) Determine how much time is required to increase the electron’s speed from rest to 0.01c

1) 6.75×10-11 s 2) 1.35×10-12 s 3) 4.5×10-21 s 4) 3.3×10-12 s

c) How far will electron travel within that time?

1) 1×10-6 m 2) 2×10-6 m 3) 4×10-6 m 4) 2.25×10-6 m

(d) Calculate the momentum of the electron moving at speed 0.93c (c is speed of light)

1) 5.71×10-22 m/s 2) 6.83×10-22 m/s 3) 3.72×10-25 m/s 4) 2.51×10-22 m/s

(e) Determine how much time is required to increase the electron’s speed from 0.93c to 0.99c.

1) 6.05×10-10 s 2) 8.1×10-12 s 3) 3.02×10-10 s 4) 6.05×10-12 s

(f) How far will electron travel within that time?

1) 0.192 m 2) 0.174 m 3) 0.129 m 4) 2.33×10-2 m

g) Is your answer to (f) approximate or exact? Briefly explain:

Problem 10 A spring has a length of 12 cm when relaxed, and a length of 17 cm when stretched by a force of magnitude 50 N. (a) What is the stiffness ks of this spring?

1) 10 N/m 2) 132 N/m 3) 1320 N/m 4) 1000 N/m

(b) This same spring is then compressed by an unknown force so that the length of the spring becomes 9 cm. What is the magnitude of this force?

1) -30 N 2) 30 N 3) 60 N 4) -60 N

Problem 11. Two sticky balls with masses m1 = 2 kg and m2 = 5 kg traveling at speeds

1v! = 〈20, 0, -14〉

m/s and 2v! = 〈-1, 7,0〉 m/s, respectively, collide and stick together. What is the final

velocity of the stuck-together balls?

(a) vx = (b) vy = (c) vz = 1) 3 m/s 1) 5 m/s 1) 4 m/s 2) 5 m/s 2) 1 m/s 2) -4 m/s 3) 9 m/s 3) -1 m/s 3) -14 m/s 4) 9.5 m/s 4) -7 m/s 4) -14 m/s

Problem 12. Please show complete solution, list approximations and provide your reasoning for this problem. State any approximations, pay attention to units and vectors. At t=0 a star of mass 4×1030

kg has velocity 〈7×104, 6×104, -8×104〉 m/s and is located at 〈2.00×1012, -5.00×1012, 4.00×1012〉 m relative to the center of a cluster of stars.There is only one nearby star that exerts a significant force on the first star. The mass of the second star is 3×1030 kg, its velocity is 〈2×104, -1×104, 9×104〉 m/s, and it is located at 〈2.03×1012, -4.94×1012, 3.95×1012〉 m relative to the center of the cluster of stars. (a) At t=1×105 s, what is the approximate momentum of the first star? (b) At t=1×105 s, what is the approximate position of the first star? (c) Discuss briefly in what ways your results for (a) and (b) may be approximate.

(d) Suppose you were asked to find the position of the first star at t=1×1010 s. Discuss briefly if the method you used in (a) and (b) would work or not and why. Explain briefly how you could use a computer to get around these difficulties.

Equation sheet Exam I, Phys172H, fall06

f i

avg

f i

r rrv

t t t

!"= #" !

! !!!

p mv!=! !

2

1

1v

c

! =

" #$ % &' (

!

,total ext netp F t! = !!!

0system surroundingsp p! + ! =

!! !

2 1 on 2by1 2 12

2 1

ˆgrav

m mF G r

r!

!

= !

!

!

2 1elec on 2by1 2 12

0 2 1

1ˆ

4

q qF r

r!"#

#

=

!

!

spring SF k s=

!

,2

ix fx

avg x

v vv

+=

2

/

1

p mv

p

mc

=

! "+ # $% &

!!

!

211

2

29

2

0

8

24

Earth

6

Earth

31

electron

27

proton

neutron proton

N?m6.7 10

kg

1 N?m9 10

4 C

3 10 m/s

9.8 N/kg

6 10 kg

6.4 10 m

9 10 kg

1.7 10 kg

G

c

g

M

R

m

m

m m

!"

#

#

#

= $

= $

= $

=

= $

= $

= $

= $

%

on by Egrav m MF gm= !

! !

1 kg = 2.2 pounds

1 inch = 2.54 cm

1 foot = 30.5 cm

1 mile = 1609 m