0 5 10 15 20 25 30 0 2 4 6 Time (s) X (m) 8

P211 Final Sample 1
1) The figure below shows the position versus time for a particle. Around what time(s) is the particle
subject to a negative acceleration?
X (m)
30
25
20
15
10
5
0
0 2 4 6
Time (s)
8
A) From 6 to 8 s only B) Around 2 and 6 s C) Around 2, 4 and 6 s
D) Around 6 s only E) Not at any times shown here
2) A 2000 kg truck traveling North at a speed of 6 m/s makes a 90° turn in a time of 4 s and emerges
from this turn going East with a speed of 6 m/s. The turn does not necessarily follow a circular arc.
What is the magnitude of the average force on the truck during this turn? (Hint: what is the velocity
change along the N-S direction? along the E-W direction?)
A) 19600 N B) 4240 N C) 3600 N
D) 6420 N E) 670 N
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P211 Final Sample 1
3) How fast would an 80 kg student need to run to have the same linear momentum as a 1600 kg car
moving at 3.6 km/h?
A) 2.2 m/s B) 10 m/s C) 20 m/s
D) 36 m/s E) 43 m/s
4) A 10 kg mass sliding on a frictionless surface explodes into two pieces, one with mass 4 kg
traveling North with speed 3 m/s, and another with mass 6 kg traveling 30° North of East with speed
5 m/s. What was the original speed (velocity magnitude) of the 10 kg mass?
A) 3.17 m/s B) 3.75 m/s C) 2.68 m/s
D) 6.08 m/s E) 6.77 m/s
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P211 Final Sample 1
5) Two masses are connected as shown in the figure. The system is released from rest and mass A
falls to the floor through a distance of 1 m. The table and pulley are frictionless. What is the kinetic
energy of mass A just before it reaches the floor?
B
10 kg
A
2 kg
1 m
A) 2.21 J B) 3.27 J C) 5.00 J
D) 19.6 J E) 39.0 J
6) A 1 kg block slides on a fixed frictional surface, as shown in the figure below. The coefficient of
kinetic friction is μ k = 0.90, and the slope angle is 60°.
What is the magnitude of the acceleration of the block (parallel to the surface) if it is sliding
downhill? Remember that sin(60°) = 0.866 and cos(60°) = 0.5 .
A) 2.53 m/s 2 B) 9.81 m/s 2 C) 4.08 m/s 2
D) 12.9 m/s 2 E) 7.82 m/s 2 Page 3

P211 Final Sample 1
7) A block A of mass m A lies on a horizontal table in contact with a block B of mass m B . An
external force F is applied to block B, as shown on the figure below, such that both blocks are
sliding to the left. A coefficient of kinetic friction μ k is present between either block and the table.
What is the acceleration of block A?
Block A
mass m A
Block B
mass m B
Force F
μ k
A)
F
m A
B)
F − μ
km
m
A
A
g
C)
F − μ
km
Bg
m
B
D)
F − μ
km
Ag
m + m
A
B
E)
F − μ
k
(m
A
+ m
m + m
A
B
B
)g
8) As the figure shows, a 4.4 kg block is accelerated by a compressed spring whose spring constant
is 320 N/m. After leaving the spring at the spring's relaxed length, the block travels over a horizontal
surface, with a coefficient of kinetic friction of μ k = 0.25, for a distance of 7.8 m before stopping.
Through what distance was the spring compressed before the block began to move?
A) 0.184 m B) 0.361 m C) 0.512 m
D) 0.725 m E) Insufficient information has been provided
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P211 Final Sample 1
9) If a 0.2 kg ball is dropped from rest from a height of 2 m above the floor, it rebounds only up to
1.5 m, because the collision with the floor is not perfectly elastic and some energy is lost. What is
the magnitude of the impulse, or momentum change, imparted on the ball by the collision with the
floor? (Hint: find the magnitude and direction of the momentum just before, and just after, the
collision with the floor.)
A) 0.168 kg m/s B) 2.34 kg m/s C) 4.03 kg m/s
D) 7.23 kg m/s E) 11.7 kg m/s
10) You are sitting still in a room taking a Phys 211 exam. What is the magnitude of your linear
velocity due to the Earth’s rotation? The Earth has a rotation period of 23.93 hours, is approximately
a sphere of mean radius R E = 6371 km, and State College is at a latitude of θ = 40.8º North, as
shown in the figure. (Hint: what is the radius R SC of the circular motion of State College around the
Earth’s axis of rotation?)
A) 352 m/s (787 mph)
B) 465 m/s (1040 mph)
C) 2830 m/s (6331 mph)
R SC
R E
State College
D) 5320 m/s (11901 mph)
θ
E) 9.8 m/s (21.9 mph)
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P211 Final Sample 1
11) An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough
that any person inside is held against the wall when the floor drops away. The coefficient of static
friction between the person and the wall is μs, and the radius of the cylinder is R.
The maximum period of revolution T such that a person won't slide down the wall is:
A)
Rμ
s
T =
2
4π
g
B)
T =
4π
2
Rμ
g
s
ω
2
C) T = 4π
Rμ
g
s
R
N
F s
D)
T =
4π
2 Rg
μ
s
F g
E)
T =
4π 2 μ
g
s
12) Wheel A of radius r A = 5 cm is coupled by belt B to wheel C of radius r C = 24 cm. Wheel A
increases its angular speed from rest at a constant rate of α A = 3.30 rad/s 2 . How long does it take
wheel C to reach a rotational speed of ω C = 50 rev/s, assuming that the belt B does not slip?
A) 40 s B) 145 s C) 457 s
D) 665 s E) 914 s
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P211 Final Sample 1
13) Each of the three helicopter rotor blades shown in the figure below is 5.20 m long and has a
mass of 210 kg. The rotor is rotating at 200 rev/min (20.94 rad/s).
If each blade can be considered to be a thin uniform rod, what is the kinetic energy of rotation of the
entire blade assembly?
A) 4.30 × 10 4 J B) 1.29 × 10 5 J C) 6.55 × 10 5 J
D) 1.24 × 10 6 J E) 3.92 × 10 6 J
14) A merry-go-round of radius R = 2 m has a moment of inertia I = 200 kg m 2 , and is rotating at ω
= 4 rev/min. A child whose mass is m = 30 kg jumps onto the edge of the merry-go-round, heading
directly toward the center at 6 m/s. What is the new angular speed of the merry-go-round
immediately after the child has boarded it?
A) 1.76 rev/min B) 3.64 rev/min C) 2.50 rev/min
D) 6.40 rev/min E) 4.00 rev/min
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P211 Final Sample 1
15) A cylinder of mass M = 1.5 kg can rotate about its central axis through point O. Forces are
applied as in the figure below: F 1 = 12 N, F 2 = 8 N, F 3 = 4 N, and F 4 = 5 N.
Also, R 1 = 5 cm and R 2 = 10 cm. The cylinder is solid, has uniform density and radius 10 cm.
What is the magnitude of the angular acceleration of the cylinder, assuming that the forces
maintain their same angles relative to the cylinder during the rotation? (Hint: what is the total torque
on the cylinder from all forces?)
A) 19.03 rad/s 2 B) 26.67 rad/s 2 C) 81.48 rad/s 2
D) 101.3 rad/s 2 E) 240.7 rad/s 2
16) A hollow cylinder and a solid cylinder have the same diameter and the same mass. Each is
placed at rest at the top of a rough inclined plane (with friction!) and each rolls without slipping to
the bottom. Which object has the lesser center of mass velocity when it reaches the bottom of the
plane? (Hint: the moment of inertia of a solid cylinder is smaller than that of a hollow cylinder of the
same mass and diameter.)
A) The solid cylinder.
B) The hollow cylinder.
C) They have the same speed.
D) Impossible to say, since it depends on the angle of the ramp.
E) Impossible to say, since it depends on the coefficient of static friction between the cylinders and
the ramp.
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P211 Final Sample 1
17) A mass of 5 kg is hanging from the beam shown in the figure, at a distance of 2 m from a wall.
The beam is connected to the wall via a hinge free to rotate frictionlessly. The beam has a uniform
mass distribution, a length of 5 m and a total mass of 20 kg. What is the magnitude of the force F at
point A necessary for the system to be in equilibrium? (Hint: there must be no net force on the
system or torque about the hinge.)
5 m
A
F
20 kg
5 kg
2 m
Hinge
Wall
A) 39N B) 78 N C) 103 N
D) 118 N E) 490 N
18) A skater extends her arms horizontally, holding a 2 kg mass in each hand. She is rotating about a
vertical axis with an angular velocity of 1 rev/s. If she pulls her hands in towards the center of her
body, approximately what will the final angular velocity be if her own moment of inertia remains
approximately constant at 5 kg m 2 , and the distance of the masses from the axis changes from 1 m to
0.2 m?
A) 12 rev/s B) 9 rev/s C) 6 rev/s
D) 3 rev/s E) 1.7 rev/s
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P211 Final Sample 1
19) Two blocks (m = 2 kg and M = 9 kg) and a spring (k = 160 N/m) are arranged on a horizontal,
frictionless surface as shown in the figure below. The coefficient of static friction between the two
blocks is μ s = 0.4. What is the maximum possible amplitude of simple harmonic motion of the
spring-blocks system if no slippage is to occur between the blocks?
A) 0.049 m B) 0.221 m C) 0.319 m
D) 0.270 m E) 0.156 m
20) An unknown mass M in a spring-mass system is attached to a massless spring of unknown
spring constant k. The spring is stretched by a distance of 10 cm, at which point the mass is released
from rest and oscillates back-and-forth on a frictionless table. If the period T of the oscillations is
measured to be 2s, what is the maximum speed of the mass as it passes through the equilibrium
position (at which point the spring is neither stretched nor compressed)?
A) 0.052 m/s B) 0.125 m/s C) 0.314 m/s
D) 0.781 m/s E) 1.76 m/s
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P211 Final Sample 1
21) A flying saucer deep in interstellar space, free of external forces, rotates about its symmetry axis
with angular velocity ω. The aliens inside the saucer rearrange the furniture to make room for a
Christmas tree they have just procured from Elvis. As a result the angular velocity of the saucer
increases to 2ω. If originally the rotational kinetic energy of the saucer was K, after the
rearrangement its new rotational kinetic energy is:
A) K/4 B) K/2 C) K
D) 2K E) 4K
22) A block of mass M = 4 kg is resting on a frictionless table and is attached to an uncompressed,
unstretched spring (k = 460 N/m) fixed to a wall at the other end, as in the figure below. A bullet of
mass m = 0.06 kg is fired into the block in a direction parallel to the alignment of the spring, with a
speed of v b = 100 m/s, and is embedded in the block. What is the amplitude x m of the resulting
simple harmonic motion? (Hint: energy is not conserved during the collision between the bullet and
the block, but momentum is; during oscillations, energy is conserved, but not momentum.)
x = 0 x = 0
−x m
+x m
M
v b
m
M+m
Initially
Finally
A) 0.052 m B) 0.139 m C) 0.211 m
D) 0.876 m E) 1.74 m
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P211 Final Sample 1
23) The diagram represents a snapshot of a standing transverse wave on a flexible string
taken when the displacement is at a maximum. The string is L = 2 m long with tension
F T = 9 N. The total mass of the string is m = 0.050 kg. What is the period T of the
oscillations? (Hint: the wave velocity is linked to the period via: v = λ / T )
A) 0.0037 s B) 0.023 s C) 0.053 s
D) 0.15 s E) 0.75 s
24) Vulcan, a hypothetical planet, has a mass of 6 × 10 23 kg, a radius of 3 × 10 6 m, and no
atmosphere. A 6 kg space probe is to be launched vertically from its surface. If the probe
is to achieve a maximum distance of 12 × 10 6 m from the center of Vulcan (at which
point it would halt briefly before starting to fall back towards Vulcan), with what initial
kinetic energy must it be launched from the surface of Vulcan? (Hint: the total energy,
i.e., kinetic plus gravitational potential, is conserved, and remember that
G = 6.67 × 10 −11 N m 2 / kg 2 .)
A) 1.2 × 10 9 J B) 3.0 × 10 7 J C) 8.0 × 10 7 J
D) 6.0 × 10 7 J E) 5.0 × 10 7 J
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P211 Final Sample 1
25) The transverse displacement for a standing wave on a string is given by:
y(x,t) = A sin(kx) cos(ωt) , with A = 2.1 m, k = π/2 m −1 , ω = 2.0 rad/s . The transverse
velocity of a piece of the string at x = 5.0 m at time t = π/2 s is most nearly given by
d
cos aθ
= −a sin aθ
and
which of the following? (Hint: remember that [ ( )] ( )
d
dθ
[ sin( aθ)
] = + a cos( aθ)
A) 0 m/s
B) 4.2 m/s in the +y direction
C) 4.2 m/s in the −y direction
D) 8.4 m/s in the +y direction
E) 8.4 m/s in the −y direction
dθ
where “a” is a constant.)
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P211 Final Sample 1
Answer key
1) B
2) B
3) C
4) B
5) B
6) C
7) E
8) D
9) B
10) A
11) B
12) C
13) D
14) C
15) B
16) B
17) D
18) E
19) D
20) C
21) D
22) B
23) C
24) D
25) A
Page 14