PHYSICS 221
Fall 2006
EXAM 1: October 4 2006 8:00pm—10:00pm
Name (printed): ______________________________________________
ID Number: _________________________________________________
Recitation Instructor: _________________________
Section #_______
INSTRUCTIONS:
This exam contains 30 equally weighted multiple-choice questions. Choose one answer only
for each question. Choose the best answer to each question. Answer all questions.
Allowed material: Before turning over this page, put away all materials except for pens, pencils,
erasers, rulers, your calculator. There is a formula sheet attached at the end of the exam. Other
copies of the formula sheet are not allowed.
Calculator: In general, any calculator, including calculators that perform graphing numerical
analysis functions, is permitted. Electronic devices that can store large amounts of text, data or
equations are NOT permitted. If you are unsure whether or not your calculator is allowed for the
exam, ask your TA.
Examples of allowed calculators: Texas Instruments TI-30XII/83/83+/89, 92+
Casio FX115/250HCS/260/7400G/FX7400GPlus/FX9750 Sharp EL9900C.
Examples of electronic devices that are not permitted: Any laptop, palmtop, pocket
computer, PDA or e-book reader.
How to fill in the bubble sheet:
Use a number 2 pencil. Do NOT use ink. If you did not bring a pencil, ask for one.
Write and fill in the bubbles corresponding to:
- Your last name, middle initial, and first name.
-   Your ID number (the middle 9 digits on your ISU card)  
- Special codes K to L are your recitation section. (Honors section, please enter 24)
Please turn over your bubble sheet when you are not writing on it.
If you need to change any entry, you must completely erase your previous entry. Also, circle
your answers on this exam booklet. Before handing in your exam, be sure that your answers
on your bubble sheet are what you intend them to be. You may also copy down your answers on
a piece of paper to take with you and compare with the posted answers. You may use the table at
the end of the exam for this.
When you are finished with the exam, place all exam materials, including the bubble sheet, and
the exam itself, in your folder and return the folder to your recitation instructor.
No cell phone calls allowed. Either turn off your cell phone or leave it at home. Anyone
answering a cell phone must hand in their work; their exam is over.
Best of luck, Paula Herrera and Anatoli Frishman
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YOU SHOULD ASSUME THAT
AIR RESISTANCE IS NEGLIGIBLE
IN ALL PROBLEMS.
G G
G
G G G
1. If the vectors P , Q and R satisfy the relations P + Q = R and P 2 + Q 2 = R 2 , what is
G
G
the angle between P and Q ?
a.
b.
c.
d.
e.
0º
15º
30º
90º
120º
G
G
2. Consider the vectors A and B shown in the diagram below lie in the x-y plane. Both
G G
vectors have the same magnitude A = B = 3. The scalar product A ⋅ B is:
y
3
G
A
x
30º
30º
a.
b.
c.
d.
e.
7.8
4.5
3.0
9.0
15.6
3
G
B
2
3. An automobile travels on a straight road for 40 km at 30 km/h. It then continues in
the same direction for another 40 km at 60 km/h. What is the average speed of the car
during this 80 km trip?
a.
b.
c.
d.
e.
40 km/h
45 km/h
50 km/h
55 km/h
None of the above
4. An object moves along the x-axis. The graph of its position versus time is shown
below. At which of the four labeled points (P, Q, R, S) is the acceleration zero?
a.
b.
c.
d.
e.
P, Q, R and S
P, Q, S
R only
P and S
Q only
3
5. A car is traveling at 30 m/s. The stoplight is 100 m from the car. What is the
magnitude of the acceleration needed to stop the car at the light? Assume the
acceleration is constant.
a.
b.
c.
d.
e.
3.0 m/s2
3.5 m/s2
4.0 m/s2
4.5 m/s2
5.0 m/s2
6. The position of a particle along the x-axis as a function of time is given by the
expression: x(t) = at3 + bt + c where a = 4.0 m/s3, b = 2.0 m/s and c = 5.0 m. What is
the acceleration of the particle at the time t = 4.0 s?
a.
b.
c.
d.
e.
0 m/s2
24 m/s2
48 m/s2
96 m/s2
190 m/s2
4
7. Ball #1 is thrown vertically upwards with speed v0 from the top of a building of
height h and hits the ground with speed v1. Ball #2 is thrown vertically downwards
from the same place with the same speed v0 and hits the ground with speed v2. Which
one of the following statements is true?
a.
b.
c.
d.
e.
v1> v2
v1= v2
v1< v2
It depends on which ball is more massive
It depends on the relation between v0, g and h.
8. A ball is thrown downward from the top of a building with initial speed 25 m/s. It
strikes the ground after 2.0 s. How high is the building?
a.
b.
c.
d.
e.
30 m
40 m
50 m
60 m
70 m
5
9. A person kicks a soccer ball off level ground at an angle of 45° above the horizontal.
In order for the ball to reach a maximum height of 30 m above the ground during its
flight, what must be the initial speed of the soccer ball?
a.
b.
c.
d.
e.
25 m/s
29 m/s
34 m/s
37 m/s
41 m/s
10. A cannon ball is fired at an angle of 30º to the horizontal on level ground with an
initial speed of 98 m/s. How long will the cannon ball remain in the air?
a.
b.
c.
d.
e.
5s
10 s
15 s
20 s
The answer depends on the mass of the cannon ball
6
11. Which of the following is true for the angular acceleration and the magnitude of the
acceleration for uniform circular motion? (R - radius of the circle)
a.
b.
c.
d.
e.
Angular acceleration = 0
Angular acceleration ≠ 0
Angular acceleration = 0
Angular acceleration = 0
None of the above
and
and
and
and
a = v2/R
a=0
a > v2/R
a=0
12. A straight 100-m wide river flows at a speed of 3.0 m/s with respect to the bank. A
canoe is paddled at a speed of 5.0 m/s with respect to the water. The trajectory of the
canoe is directly across the river, perpendicular to the flow of water, as viewed from
the bank. How long does it take for the canoe to cross the river?
a.
b.
c.
d.
e.
20 s
25 s
30 s
33 s
50 s
7
13. An elevator with a mass of 2000 kg is given an upward acceleration of 1.2 m/s² by a
cable. What is the tension in the cable?
a.
b.
c.
d.
e.
10 kN
12 kN
16 kN
17 kN
22 kN
14. Four blocks of masses m1 = 1.0 kg, m2 = 2.0 kg, m3 = 3.0 kg, m4 = 4.0 kg are on a
frictionless horizontal surface as shown in the figure below. The blocks are
connected by ideal massless strings. A force FL = 30 N is applied to the left block and
is directed to the left. Another force FR = 50 N is applied to the right block, and is
directed to the right. What is the magnitude of the tension T in the string between m2
and m3?
T=?
FL=30 N
m1 =
1.0 kg
a.
b.
c.
d.
e.
m2 =
2.0 kg
m3 =
3.0 kg
m4 =
4.0 kg
FR=50 N
T=6N
T = 20 N
T = 30 N
T = 36 N
T = 50 N
8
The situation below refers to the next two questions:
A block of mass M = 5.0 kg on an incline is attached to a rope that goes through a pulley
on top of the incline. A counterweight of mass m is attached to the other end of the rope
(see figure). The incline makes an angle θ = 30º with the horizontal. The coefficients of
kinetic and static friction between the block and the incline are µk = 0.30 and µs = 0.40.
The pulley and the rope are ideal and massless. The system is initially at rest.
block
m
M
θ
counterweight
15. Determine the maximum value of m (the mass of the counterweight) so that the block
does not move up the incline.
a.
b.
c.
d.
e.
1.2 kg
2.5 kg
3.8 kg
4.2 kg
4.6 kg
16. The string is cut so the block and the weight can move independently of each other.
Find the acceleration of the block on the incline.
a.
b.
c.
d.
e.
1.2 m/s2
2.4 m/s2
4.9 m/s2
7.4 m/s2
9.8 m/s2
9
The situation below refers to the next two questions:
A 20-kg box is pulled at constant speed for 10 m along a horizontal surface by a rope that
makes an angle of 15° with the horizontal. The tension in the rope is 100 N.
15°
17. Find the coefficient of kinetic friction between the floor and the box.
a.
b.
c.
d.
e.
0.26
0.38
0.49
0.57
0.64
18. Find the work by the tension in the rope.
a.
b.
c.
d.
e.
500 J
680 J
970 J
1000 J
1960 J
10
19. A 1.2 –kg lantern hangs from the ceiling and the wall with two cables as shown
below. Determine the tension in cable 2.
a.
b.
c.
d.
e.
4.2 N
5.3 N
6.8 N
8.7 N
12 N
60°
Cable 1
90°
Cable 2
20. Blocks A and B (mA>mB) are pushed by a horizontal force F along a horizontal
surface. The system has an acceleration to the right.
a
Compare the magnitude of the following forces:
F
fB, the friction by the floor on B;
A
B
NB, the force by block A on block B
NA, the force by block B on block A
a.
b.
c.
d.
e.
fB < NB = NA
fB < NB < NA
fB > NB = NA
fB > NB > NA
fB = NB > NA
11
The situation below refers to the next two questions:
A block of mass 1.5 kg is pushed against a spring as shown in the figure. The spring
compression is 4.0 cm and the spring constant is 6000 N/m. When the system is
released from rest, the block slides along a horizontal section and then up an incline
that makes an angle of 30° with the horizontal. All surfaces are frictionless and the
transition from the horizontal to the incline is perfectly smooth.
m = 1.5 kg
h
θ = 30º
21. Determine h, the maximum height above its initial level that the block will reach on
the incline.
a.
b.
c.
d.
e.
21 cm
33 cm
45 cm
52 cm
71 cm
22. Find the net work on the block during this motion (from the moment it is released to
the point of maximum height on the incline).
a.
b.
c.
d.
e.
−9.8 J
−4.8 J
0
4.8 J
9.8 J
12
23. A 100-g particle moves along the x axis under the effects of a force Fx = ( −5.0 N/s ) t .
At t = 0, the velocity of the particle is 10 m/s in the positive x direction. Find the xcomponent of the velocity of the particle at t = 1.2 s.
a.
b.
c.
d.
e.
−26 m/s
−36 m/s
−50 m/s
−62 m/s
−72 m/s
24. Two blocks with masses mA = 2 mB are released from the top of two frictionless
inclines as shown below. On which ramp will the block move the fastest at the
bottom of the ramp?
mA = 2 mB
Ramp A
mB
Ramp B
a. On ramp A, because the mass of block A is larger.
b. On ramp A, because the ramp is longer and thus the block accelerates for a
longer time
c. On ramp B because the ramp is steepest.
d. On ramp B, because the mass is smaller, so the acceleration is largest.
e. Both blocks have the same speed at the bottom of the ramps.
13
The situation below refers to the next two questions:
A 10-kg box is placed on top of a 12-kg sled that can move without friction on a frozen
lake. The sled is pulled with a horizontal rope. The box and the sled move together with
an acceleration of 2.0 m/s2.
25. What is the tension in the pulling rope?
a.
b.
c.
d.
e.
20 N
24 N
44 N
100 N
120 N
26. What is the magnitude of the friction between the box and the sled?
a.
b.
c.
d.
e.
10 N
20 N
30 N
40 N
It cannot be determined because the coefficient of friction is not given.
14
27. A pendulum with a 1.0-kg bob and a 3.0-m long, very light rope hangs from the
ceiling. Initially, the rope makes an angle of 40º with the vertical. The bob is released
from rest. Find its speed at the bottom of its trajectory.
a.
b.
c.
d.
e.
3.7 m/s
4.7 m/s
5.7 m/s
6.7 m/s
7.7 m/s
28. A bucket attached to a string moves in a vertical circle. There is a rock inside the
bucket. Which of the options below best describes the direction of the net force on the
rock at the bottom of the trajectory?
Direction
of motion
a
b
c
d
e. The net force is zero
15
29. A person throws a ball off a cliff with initial speed v0. Depending on the initial angle,
the trajectory will be different. Let v1, v2 and v3 be the speed of the ball right before
hitting the ground in trajectories 1, 2 and 3 shown below. Rank these speeds.
v0
3
v0
v0
2
1
a.
b.
c.
d.
e.
v1 >
v1 >
v1 <
v1 <
v1 =
v2 >
v3 >
v2 <
v3 <
v2 =
v3
v2
v3
v2
v3
30. A box that weighs 500 N sits on the floor of an elevator. The elevator is moving
upwards at a constant velocity of 5.0 m/s. What is the magnitude of the net force
acting on the box?
a.
b.
c.
d.
e.
1000 N
750 N
500 N
250 N
0N
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Here you can write down your answers and keep this page to compare with the posted
solutions.
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