- Which of the following quantities has the same dimensions as kinetic
energy,
1
2mv
2? Note:
x and
h are lengths,
a is acceleration,
g is acceleration due to gravity and t is time.
a) ma b) mvx c) mvt d) mgh e) mgt - At t = 0, a particle leaves the origin with a velocity of 12 m/s in
the positive
x direction and moves in the xy plane with a constant
acceleration of (
−2.0ˆi + 4.0ˆj) m/s - At the instant the
y coordinate of
the particle is 18 m, what is the
x coordinate of the particle?
a) 30 m
b) 21 m
c) 27 m
d) 24 m
e) 45 m - Taking the acceleration due to gravity to be 9.8 m/s
2, which of the
following statements is false for a body falling freely from rest near the
surface of the earth? (Ignore air resistance.)
a) after 1 second, the body has fallen 9.8 meters.
b) after 3 seconds, its speed is 29.4 meters per second.
c) during each time interval of 1 second, its speed changes by 9.8
meters per second.
d) after 2 seconds, the body has fallen 19.6 meters.
e) The force on the body remains constant. - An automobile moving along a straight track changes its velocity from
40 m/s to 80 m/s in a distance of 200 m. What is the (constant)
acceleration of the vehicle during this time?
a) 8.0 m/s
2
b) 9.6 m/s
2
c) 12 m/s
2
d) 6.9 m/s
2
e) 0.20 m/s
2 - At t = 0 a particle leaves the origin with a velocity of 5.0 m/s in the
positive
y direction. Its acceleration is given by
a = (3.0i − 2.0j)m/s
2
.
At the instant the particle reaches its maximum
y coordinate how far
is the particle from the origin?
a) 11 m
b) 16 m
c) 22 m
d) 29 m
e) 19 m - The velocity vs. time graph describes the motion of a snowboarder.
The snowboarder’s acceleration (in m/s
2) at the time of t = 2 s is
(explain your reasoning on the front cover sheet.):
a)
− 4.5
b) 9.0
c)
− 1.5
d)
− 2.0
e) 4.5 - A 0.14-km wide river flows with a uniform speed of 4.0 m/s toward
the east. It takes 20 s for a boat to cross the river to a point directly
north of its departure point on the south bank. What is the speed of
the boat relative to the water?
a) 5.7 m/s
b) 8.5 m/s
c) 8.1 m/s
d) 7.0 m/s
e) 6.4 m/s
2
Part 2 - You hold a tennis racket vertically in your hand. On the top edge of
the racket you have balanced a ball. Which statement is true?
a) The force of your hand on the racket and the force of the ball
on the racket are equal in magnitude and opposite in direction.
b) The force of the racket on your hand and the force of the ball
on the racket are equal in magnitude and opposite in directio
n
c) The force of your hand on the racket and the force of the racket
on the ball are equal in magnitude and opposite in direction.
d) The force of the racket on your hand and the force of the racket
on the ball are equal in magnitude and opposite in direction.
e) The force of your hand on the racket and the force of the racket
on your hand are equal in magnitude and opposite in direction. - An 80-kg person slides on a patch of ice, pulled by a horizontal rope.
The coefficient of friction of the person with the ice is 0.05. If the
person sliding is not accelerating, the tension in the rope is
a) 800 N b) 4 N c) 8 N d) 20 N e) 39 N - A mass M = 5.6 kg on a horizontal table is pulled by a horizontal
string that passes over a frictionless massless pulley to a free-hanging
mass m = 3.4 kg. The coefficient of friction between M and the table
is 0.28. The acceleration of M is
a) 3.7 m/s
2
b) 2.0 m/s
2
c) 2.2 m/s
2
d) 0.20 m/s
2
e) 0.49 m/s
2 - A conical pendulum consists of a 2.0-kg bob suspended by a massless
string of length 3.0 m. The bob moves in a circle in the horizontal
plane such that the angle of the string to the vertical is constant at
20
◦. The tension in the string is
a) 19 N
b) 21 N
c) 23 N
d) 25 N
e) 27 N - A mass m slides down a loop-the-loop
track shown. The track is frictionless and the mass
m, which is released
from rest a height
h above point A,
just makes it around the track without loosing contact at point C. What
is the value of
h in terms of r? Neglect
air resistance.
a) 2.0r
b) 1.5r
c) 2.2r
d) 2.4r
e) 2.5r
h
r
C
A - A train engine pulls a freight train with mass 10
7 kg with a force of
500 kN, starting from rest. After one minute the speed of the train is
a) 0.05 m/s
b) 0.3 m/s
c) 3 m/s
d) 0.003 m/s
e) 5 m/s - Two balls, projected at different times so they don’t collide, have trajectories A and B, as shown below. Which statement is correct?
a) Ball B’s initial speed must be
greater than that of ball A.
b) Ball A is in the air for a longer
time than ball B.
c) Ball B is in the air for a longer
time than ball A.
d) Ball B has a greater acceleration than ball A.
e) Ball A has a greater acceleration than ball B.
3 - A mass of 2.0 kg is placed at rest on an inclined plane making an angle
of 40
◦ with the horizontal and slides down a distance of 15 m, as shown.
Its speed at the bottom is 12 m/s. How much of its mechanical energy
is lost due to friction? (in J)
a) 45
b) 23
c) 189
d) 144
e) 72 40
o
15 m
2 kg - A 1-kg mass is attached to a massless spring with constant of 100 N/m,
and hangs from the ceiling as shown. Initially the mass is at rest in the
unextended position of the spring, and then the mass is released. The
mass falls until the spring is extended to a maximum, then bounces
back up. The maximum extension of the spring is
a) 0.2 m
b) 0.1 m
c) 0.4 m
d) 1.0 m
e) 2.0 m 1 kg
100 N/m - A bumper on a car can be thought of as a spring with constant k =
900 kN/m. If a 1000-kg car with such a bumper is coasting at 3 m/s
and hits a wall, what will the maximum compression of the bumper
be? Assume the collision is elastic, and that the bumper has negligible
mass compared with the car.
a) 1 cm
b) 10 cm
c) 1 m
d) 1 mm
e) 0.1 mm - A boy launches a rock straight up with an elastic slingshot by pulling it
a certain distance
x from the unstretched position. The rock reaches a
maximum height
h above the point of launch, where
h is much greater
than
x. If the boy then launches the same rock by stretching the
slingshot by 2
x, the maximum height will be nearest
a)
h
b)
√
2h
c) 2
h
d) 4
h
e) (need mass of rock, spring constant of slingshot) - A mass of 2.0 kg is moving south with a speed of 4.0 m/s while a mass
of 5.0 kg is moving east at 3.0 m/s. They collide at the origin and stick
together as shown. In what direction does the combined mass of 7.0
kg move? (A line pointing horizontally towards the right of the figure
is defined as 0
◦ and the angle is measured in the clockwise direction
from this reference direction.)
a) 114
◦
b) 62
◦
c) 47
◦
d) 15
◦
e) 28
◦ 5 kg 3 m/s
4 m/s
2 kg
4 - A 2.0 kg object, initially traveling in the +x direction with a speed of
4.0 m/s, explodes in flight into two pieces, each of mass 1.0 kg. One
piece travels at 12.0 m/s in the same direction as the 2.0 kg object was
moving initially. What is the velocity (speed in m/s, and direction) of
the center of mass of the two pieces after the explosion?
a) 8, in the −x-direction.
b) 4, in the +x-direction.
c) 6, in the +x-direction.
d) 6, in the −x-direction.
e) 12, in the +x-direction. - An 80-g particle moving with an initial speed of 50 m/s in the positive
x direction strikes and sticks to a 60-g particle moving 50 m/s in the
positive y direction. How much kinetic energy is lost in this collision?
a) 96 J
b) 89 J
c) 175 J
d) 86 J
e) 110 J - An empty rail car coasts along a track at constant velocity v and
couples to a full rail car initially at rest. If the velocity of the two cars
coupled together is v/5, the ratio of the mass of the empty car to that
of the full car is
a) 1/4
b) 4
c) 1/5
d) 5
e) need more information - A 1.2-kg ball falling vertically hits the floor with a speed of 2.5 m/s
and rebounds with a speed of 1.5 m/s. What is the magnitude of the
impulse exerted on the ball by the floor?
a) 9.6 N-s
b) 4.8 N-s
c) 6.4 N-s
d) 1.6 N-s
e) 1.0 N-s - A flywheel, initially at rest, has a constant angular acceleration. After
9 seconds the flywheel has rotated 450 rad. Its angular acceleration in
rad/s2 is:
a) 100 b) 1.77 c) 50 d) 11.1 e) 15.9 - The turntable of a record player has an angular velocity of 8.0 rad/s
at the moment when it is turned off. The turntable comes to rest 2.5 s
after being turned off. Through how many radians does the turntable
rotate after being turned off? Assume constant angular acceleration.
a) 12 rad
b) 8.0 rad
c) 10 rad
d) 16 rad
e) 6.8 rad - Two stars and two rectangles are hung from a uniform rod of mass mrod
The rod is suspended from the ceiling such that the mobile balances in
a perfectly horizontal orientation, as shown. How does the total mass
of the stars, MS, compare to the total mass of the rectangles, MR?
(Explain your reason in the front cover sheet.)
a) MS > MR
b) MS < MR
c) MS = MR
d) MS + MR = mrod
e) It impossible to compare without more information
5 - A hoop of mass M and radius R rotates about its axis of circular
symmetry with angular velocity
ω. A solid disk of mass M and radius
R rotates about its axis of circular symmetry with angular velocity 2
ω.
The ratio of the kinetic energy of rotation of the hoop to that of the
disk is
a) 1/4
b) 1/2
c) 1
d) 2
e) 4 - You are hired by a lumber company to design a machine that will
make cylindrical logs (with radius
R = 0.30 m) roll about their axis
on a horizontal surface (without slipping) at just the right angular
velocity so that they can go up an 11.5
◦ ramp that is 10 m long and
just drop into a waiting truck. At what angular velocity
ω (in rad/s)
should your machine make the logs roll?
a) 17
b) 5
c) 1.5
d) 40
e) 21 - A torque of 42 Nm gives a large wheel an angular acceleration of
0.78 rad/s - What is the moment of inertia in units of (kg m2) of the
wheel?
a) 32 b) 12 c) 5.1 d) 54 e) 0.98 - A block of mass M is hanging from a horizontal bar of length L as shown
in the figure. One end of the bar is held on the edge of a desk and the
other end is held up by a rope vertically. What is the magnitude of
the torque exerted by the rope about the edge of the desk? Assume
that the mass of the bar is negligible.
a) MgL
b) 2MgL/3
c) MgL/3
d) MgL/4
e) The answer depends on
the length of the rope.
6
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