True-false questions are worth 2 points each, three-choice multiple
choice questions are worth 3 points each, five-choice multiple choice
questions are worth 6 points each. The maximum possible score is 115.
The exam period was 90 minutes. The mean score was 86.2; the median was
89. Click here to see the formula sheet
that came with the exam.
A block m1 with mass 7 kg moves up an inclined
plane with an initial velocity v0 = 4.7 m/s. The
inclined plane is at an angle of θ = 45° from the
horizontal. The coefficient of kinetic friction between the block and
the incline is 0.25.
What is the block's velocity when it has traveled a distance D=1 meter
up the incline?
(a) 0.10 m/s
(b) 0.31 m/s
(c) 0.57 m/s
(d) 1.59 m/s
(e) 2.18 m/s
(b) stays the same.
A frictionless ramp of mass 3m is initially at rest on a
horizontal frictionless floor. A small box of mass m is placed at the
top of the ramp and then released from rest. After the box is released,
it slides down the ramp and onto the horizontal floor, where it is
measured to have a speed v, having fallen a total distance
What is the speed v of the box after it has left the ramp?
(a) less than in the previous question.
(b) the same as in the previous question.
(c) more than in the previous question
If there were kinetic friction between the ramp and the
floor, but none between the box and the ramp, the speed v of the box
after it has left the ramp, compared to its speed when both the ramp and
the floor are frictionless, would be
(b) the same.
Two discs are free to move without friction on a horizontal table.
The 0.4 kg disc is initially at the position (x = 0, y =
1.0) m, moving with velocity (vx = 3.0,
vy = 0) m/s. The 0.6 kg disc is initially at
(x = 1.5, y = 0) m, moving with velocity
(vx =0, vy =2.0) m/s. The figure
above displays the initial conditions for the two discs in the
x-, y- coordinates.
The initial velocity of the center of mass of the two-disc system
(a) (vx,vy) = (3.0,2.0) m/s
(b) (vx,vy) = (2.0,3.0) m/s
(c) (vx,vy) = (2.7,2.0) m/s
(d) (vx,vy) = (1.8,1.8) m/s
(e) (vx,vy) = (1.2,1.2) m/s
(a) less than before the collision
(b) the same as before the collision
(c) It depends on whether the collision is elastic or inelastic.
What is the maximum compression of the spring, d, after the
collision (the clay sticks to the block)?
(a) d = 0.034 m
(b) d = 0.089 m
(c) d = 0.108 m
(d) d = 0.266 m
(e) d = 0.437 m
Two eggs of mass m = 0.15 kg with initial velocity v = 3 m/s
are incident on a trampoline and on an ordinary floor. One egg makes an
elastic collision with the trampoline; the other makes a totally inelastic
collision with the floor.
If the interaction time of the egg with the trampoline is
tt = 0.1 s, what is the average force F on the
egg during the collision?
(a) F = 1.8 N
(b) F = 2.0 N
(c) F = 3.5 N
(d) F = 6.0 N
(e) F = 9.0 N
(a) tf = 0.00038 s
(b) tf = 0.0024 s
(c) tf = 0.0086 s
(d) tf = 0.0129 s
(e) tf = 0.153 s
(a) 1/3 m
(b) 2/3 m
(c) 1 m
(d) 4/3 m
(e) 5/3 m
A space capsule of mass m is launched from the surface of the
earth with a speed VE = 6.0 × 103
m/s. The radius and mass of the earth are RE = 6.37
× 106 m and ME = 5.97 ×
1024 kg respectively. Newton's gravitational constant is
G = 6.67 × 10-11 N-m2/kg2.
Neglect air resistance.
What is the maximum height Rmax measured from the
center of the earth, reached by the space capsule?
(a) Rmax = 5.73 × 106 m
(b) Rmax = 7.00 × 106 m
(c) Rmax = 8.95 × 106 m
(d) Rmax = 1.27 × 107 m
(e) Rmax = 1.72 × 107 m
(c) the same.
(a) about 2VE.
(b) about 0.01VE.
(c) about the same as VE.
Two identical masses are suspended from massless strings of equal
length. One mass is released from a height h as depicted in the
figure below. When the first mass hits the second, the two masses stick
What is the maximum height H reached by the two masses
(a) H = h / 4
(b) H = h / 2
(c) H = h
(d) H = 2 h
(e) H = 4 h
(a) smaller than H.
(b) equal to H.
(c) larger than H.
A massless spring of spring constant k = 30 N/m hangs
vertically in the earth's gravitational field. A 1 kg mass is attached
to the spring.
Measuring from the unstretched length of the spring, how much has
the gravitational potential energy of the mass changed when the spring
reaches its equilibrium length with the mass attached?
(a) 0 N-m
(b) +1.27 N-m
(c) -1.27 N-m
(d) +3.21 N-m
(e) -3.21 N-m
(a) 0 m/s
(b) 0.55 m/s
(c) 0.72 m/s
(d) 1.10 m/s
(e) 2.73 m/s
If the weight is to move up a distance h, through what
distance, D, must you pull the free end of the rope?
(a) D = h
(b) D = h/2
(c) D = 2h
(d) D = 4h
(e) D = 3h/2
Two identical blocks initially have the same
velocity V at the bottom of two ramps. The first ramp inclined
at a shallower angle (θ1) with respect to the
horizontal than the second ramp (θ2). The
maximum heights reached by the blocks are h1 and
Assume that both ramps are frictionless. Which one of these
statements is correct concerning the maximum heights reached by the
(a) h2 = h1
(b) h2 > h1
(c) h2 < h1
(a) h2 = h1
(b) h2 > h1
(c) h2 < h1
If the speeds after the collision are v1f = +3 m/s
and v2f = -2 m/s, what were their speeds
v1i and v2i before the collision?
(a) v1i = -3.00 m/s, v2i = +2.00 m/s
(b) v1i = -4.50 m/s, v2i = +1.50 m/s
(c) v1i = +2.75 m/s, v2i = -1.75 m/s
(d) v1i = -3.25 m/s, v2i = +1.75 m/s
(e) v1i = +3.25 m/s, v2i = -2.25 m/s