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Exam II, vers. 0001 - Physics 2010
NAME_______________________________________________________
Signature_____________________________________________________
Student ID #__________________________________________________
Circle your TA’s Name:
Circle the day of your recitation/lab section:
M Tu
W
Th
Fr
Circle the start time of your recitation/lab: 8am 10am Noon 2pm 4pm
Please do not open the exam until you are told to.
Your exam should have 9 pages, numbered 1 thru 9. The last sheet is for scratch paper. This exam consists of 25
questions, worth 4 points each for a total of 100 points. Fill in the bubble sheet with a #2 pencil.
Please fill out your bubble sheet according to the following instructions or you will automatically
lose 10 points. Check each box as you complete the instructions.
Please circle your TA's name and the day and time of your lab section above.
Print and bubble in your name on the bubble sheet.
Print and bubble in your student Identification Number.
Print and bubble in your Exam version, 0001 or 0002, in the upper left of your bubble sheet in the area
marked 1234.
On your bubble sheet, erase mistakes thoroughly, and make no extraneous marks
As you take the exam, show all your work on the exam and circle the correct answers on your exam.
Your circled exam answers and bubbled answers must agree.
I have read and followed the instructions above. I give my word that I have neither given nor received
unauthorized assistance on this exam.
Signature______________________________________________
Possibly useful information: Magnitude of acceleration of gravity: g = 9.8 m/s2
2
1
3
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30-60-90 triangle
2
1
45-45-90 triangle
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Possibly useful information: Magnitude of acceleration of gravity: g = 9.8 m/s2
2
1
3
30-60-90 triangle
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2
1
1
45-45-90 triangle
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1. A variable x is known to obey the following equation in which a and b are positive constants:
x
=1
ax+b
A)
b −1
a
Solve for the unknown x.
B)
a−b
b
C) 2a − b
D)
b
1− a
E) None of these.
2. The areal mass density  of a sheet of some material is defined as the mass per area of the sheet,
 = mass/area. A particular lead sheet has an areal density of  = 10 gram/cm2. What is the areal
density in units of kg/m2 ?
A) 1
B) 10
C) 100
D) 0.1
E) None of these
3. In a projectile motion problem, a student is trying to compute the time of flight (total time in the air).
She needs to solve the following equation for the time t : y = yo + voy t -
1
2
g t 2 . She sets y = 0 and
yo = 0 (since the projectile starts and ends at y = 0). What is the correct expression for the time of flight
that she derives?
2 v0 y
g
A)
B) 0 C)
D) - voy + voy 2 - 4g voy
E) 12 v0y g 2
2 v0 y
g
y
4. A projectile is fired from the top of a building at a (non-zero)
angle  above the horizontal with an initial speed vo. What is the
correct expression for the speed of the projectile at the apex of the
trajectory?
A) v 0
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B) v0 cos q
2
2
C) (v0 cos q) + (2 v 0 sin q)
vo
speed = ?

D)
v0 2 + g 2
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x
E) zero
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5. A person exerts a constant horizontal force on a large box which is on her office floor. As a result,
the box moves across the horizontal floor at a constant speed vo. The coefficient of kinetic friction
between the floor and the box is a constant K = 0.7. The magnitude of the constant horizontal force
applied by the person (pick the one statement which is always true)…
A) is greater than the magnitude of the weight of the box.
B) is the same as the magnitude of the force of sliding friction on the box from the floor.
C) is greater than the magnitude of the force of sliding friction on the box from the floor.
D) is smaller than the magnitude of the force of sliding friction on the box from the floor.
E) is the same as the magnitude of the weight of the box.
6. A stone is thrown at an angle  = 55o above the horizontal x-axis near the
surface of the earth, with an initial speed vo . If air-resistance is negligible,
which of the following v vs. t graphs best represents vx vs. t and vy vs. t.
v
vo

v
v
t
t
1
t
3
2
v
y
v
t
t
4
vx
5
vy
--------------------
A)
B)
C)
D)
E)
1
2
4
3
3
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4
1
5
5
2
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x
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7. In a tilted xy coordinate system, the direction of the acceleration vector is parallel to the x-axis,
as
r
shown. The coordinates are tilted at an angle . The magnitude of the acceleration vector is | a | = a .
What are ax and ay, the x- and y-components of the vector
r
a?
y
A) ax = 0 , ay = –a
B) ax = +a , ay = 0
C) ax = 0,
a

ay = +a
D) ax = – a cos , ay = –a sin
x
E) ax = + a cos , ay = –a sin
8. A penny of mass m is sitting on a box that is accelerating to the right, as shown. The coefficient of
static friction between the penny and the box is s .When the acceleration of the box is slowly increased,
the penny slides off just when the magnitude of the acceleration reaches amax = 15 m/s2 . However,
when the acceleration of the box is kept at ao = 10 m/s2, the penny stays in place on the box. Which of
the following statements are true when the box's acceleration is ao = 10 m/s2 and the penny stays on the
box.
penny
mass m
a
box
I. The magnitude of the force of static friction on the penny Ffric = s mg.
II. The magnitude of the acceleration of the penny is ao = 10 m/s2 .
III. The magnitude of the net force on the penny is Fnet = m ao .
A) All are true.
C) Only I and II are true.
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B) None are true.
D) Only II and III are true
E) Only I and III are true.
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9. Three vectors, X , Y ,
are shown below. Which one of the
following vector equations describes this diagram?
and Z
X

Y
r r
r
A) Y + Z = X
B) X + Y = Z
D) X + Y + Z = 0
E) None of the above equations is correct.
C) Y − Z = X
10. Two objects of mass m and 2m are attached by a massless string over a massless,
frictionless pulley as shown (an Atwood machine). A student wishes to compute the
magnitude of the tension FT in the string. After some work, she writes down the
following two correct equations:
m
2mg – FT = 2m a
FT – mg = m a
These are two equations in the two unknowns a and FT. Solve for a. The correct
expression for the magnitude of the tension is a = ...
A) g
B) (1/2) g
C) (2/3)g
D) (1/3)g
2m
E) None of these
11. A person is standing in an elevator that is moving downward
at a decreasing speed. How does the magnitude of the normal
force FN on the person's feet compare to the person's weight mg?
A) FN > mg B) FN < mg
D) impossible to tell
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C) FN = mg
moving down
|v| decreasing
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The following two questions refer to a conical pendulum, which is a mass hanging from string with the
mass moving in a circular path so that the string makes a constant (non-zero) angle  with the vertical
and sweeps out a cone.
12. At the moment when the mass is at the far left (as shown in the diagram), which free-body most
accurately represents the forces on the mass?
C)
B)
A)

D)
E)
13. In the conical pendulum shown above, how does the magnitude of the net force, Fnet , on the mass
compare to the magnitude of the tension FT in the string?
A) Fnet > FT
B) Fnet = FT
C) Fnet < FT
D) Answer depends on the speed of the mass.
14. Three blocks, each with mass m, are connected by strings and are pulled to the right along the
surface of a frictionless table with a constant force of magnitude F. The magnitudes of the tensions in
the strings connecting the masses are T1 and T2 as shown.
T2
T1
F
m
m
m
How does F compare to T2 ?
A) F = T2
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B) F = 2 T2
C) F = (3/2) T2
D) F = 3 T2
E) F = (2/3) T2
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15. A mass m is pulled along the surface of a frictionless
table by a constant external force of magnitude Fext at some
non-zero angle  above the horizontal. The magnitude of the
normal force exerted by the table on the mass is FN .
Fext
no friction

m
What is the magnitude of the net force on the mass m?
A) Fext + FN + mg
B) FN – mg + Fext sin
C) zero
16. Two cars, labeled A and B, are traveling along a
long straight road. The road runs east and west. East is
chosen as the positive direction; west is the negative
direction. The curves of velocity vs. time for the two
cars are shown in the graph. Note that the curves cross at
t = to. Consider the following statements: During the
time period shown in the graph,
D)Fext sin
E) None of these
v
A
B
to
I. one car is always moving East and the other car is always moving West.
II. the net force on each car is non-zero and always towards the East.
III. both cars have the same velocity at time t = to.
How many of the statements must be true, given the information in the graph?
A) All are true
B) None are true
C) exactly one statement is true
D) exactly 2 statements are true
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t
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17. A car, moving at constant speed, travels through the bottom of a valley, as shown. The valley is
shaped like part of a circle. At the instant that the car is at the nadir (the very bottom) of the valley, how
does the magnitude of the normal force FN from the road on the car compare to the magnitude of the
weight mg of the car? A) FN > mg
B) FN = mg
C) FN < mg
18. A box of mass m = 10.0 kg is on a flat rough floor where the coefficient of static friction is S = 0.4
and the coefficient of kinetic friction is K = 0.3. A constant horizontal force of magnitude F = 50.0 N
(50.0 newtons) is being applied to the box. What is the magnitude of the net force on the box?
A) 50.0 N
B) zero
C) 20.6 N
D) 10.8 N
E) None of these.
19. An astronaut in inter-galactic space twirls a rock of mass m on a string of length R. The rock
moves in a circle with constant speed and the tension in the string is FT. [For this problem, assume no
gravity.] What is the speed v of the rock?
FT R
2p R
mR
A) 12 g FT
B) 4p 2 2
C)
D)
E) None of these.
m
FT
FT
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20. Two stars are far out in intergalactic space. The only force on each star is the gravitational force
from the other star. The stars are initially a distance R apart and are moving apart, each with an initial
speed v. Fill in the blanks: As the stars move apart, the speed of each star ______, and the magnitude of
the acceleration of each star _____.
A) decreases, increases
B) increases, decreases
v
C) increases, increases
v
R
D) decreases, decreases
E) decreases, remains constant.
21. A small rock of mass m is near a large planet of mass M. The
force of gravity on the rock from the planet has magnitude Fon rock . The
force of gravity on the planet from the rock has magnitude Fon planet.
F
What is the ratio of the size of the forces on rock ?
Fon planet
2
A) m/M
B) M/m
C) (m/M)
D) (M/m)2
M
m
E) 1 (forces have same magnitude)
v1
22. A car drives over the top of a round hill while
slowing down. The velocity vectors of the car are
shown just before (v1) and just after (v2) the car is at the
top. What is the direction of the acceleration of the car
when it is at the bottom of the valley at the position
shown by the x?
A) lower left
B) straight up
C)lower right
D) horizontal, straight right
E) straight down
v2
B
D
A
C
E
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23. A crate of mass m up a straight incline is observed to be
sliding down an incline at a constant speed v. There is
friction between the crate and the incline. What is the
direction of the net force on the crate?
A) Parallel to the incline, down the incline
B) Straight down
C) Parallel to the incline, up the incline
D) Perpendicular to the incline, upward
E) No direction, because the net force is zero.
v = constant
m
D
A
C
B
24. A rock of mass m at the end of a string is twirled in a circle
of radius R in a vertical plane at constant non-zero speed v.
(Note that there is gravity in this problem.) When the rock is at
the bottom of its arc, how does the magnitude of the tension in
the string FT compare to the magnitude of the weight mg of the
rock?
A) FT = mg
B) FT < mg
C) FT > mg
D) The answer depends on the speed v.
down
R
v
m
25. Two horizontal forces are acting on a chunk of wood sitting on ice, as shown. The diagram shows
the forces viewed from above. F is 30.0 N (east), F is 40.0 N (north). The wood accelerates at
2
1
10 m/s2. To 2-place precision, what is the mass of the chunk of wood? (Assume that friction is small
enough to ignore.)
A) 5.0 kg
B) 0.2 kg
C) 7.0 kg
D) 250 kg
E) 0.33 kg
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F2 = 40 N
m
F1 = 30 N
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Unused questions
26. Ball A is thrown up at the same time (from the same place) as ball B, but with twice the initial speed
of ball B. How much higher does ball A rise, compared to ball B?
A) 4 times higher.
B) 3 times higher.
C) 2 times higher.
D) same height.
E) you need to know the relative masses of A and B to decide.
27. A projectile is fired from the top of a building at an angle  = 45o above the horizontal with an
initial speed vo. Consider the relative speeds of the projectile at the following points.
I. At the initial height, immediately after the projectile leaves the barrel of the gun.
II. At the apex of the trajectory.
III. At the same height as initially, during the descent.
IV. Immediately before the projectile hits the ground.
II
I
III
IV
Rank the points in order from largest speed to smallest speed
A) I > II > III > IV (speed I greater than speed speed II greater than speed III greater than speed IV)
B) I = III > IV > II (speed I equal speed III greater than speed IV greater than speed II)
C) II > I = III > IV
D) I = II = III = IV
E) IV > I = III > II
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