1. A perfectly spherical ball of mass 0.50 kg is pushed up against a massless plate fixed to
the end of a massless spring. The ball is pushed until the spring (spring constant=k1
= 12.5 N/m) is compressed by 2.0 meters. If the ball is then released from rest, the
spring will do work on the ball and accelerate it until the spring reaches its equilibrium
position. At the instant just after release (when the ball is at x0 = −2.00 m) , what is
the magnitude of the instantaneous force that the spring exerts on the ball?
a) 6.25 N
b) 12.5 N
c) 25.0 N
d) 50.0 N
e) 80.0 N
4. Now the ball slides up the track (rising a height h1 = 1.0 m above where it started from
in question 1) and flies horizontally off the edge of a cliff with velocity vc = 8.966 m/s.
If the ball falls a height h2 = 8.00 m, how far from the base of the cliff, d, does the ball
impact the ground?
a) 11.5 m
b) 11.0 m
c) 10.8 m
d) 10.4 m
e) 9.7 m
7. Now, the combined object has a mass Mtot = 2.00 kg, and it slides across a rough patch
of length ∆x with coefficient of friction µk . How much work does friction do on this
combined mass?
a) −µk Mtot g(∆x)2
b) +µk Mtot g∆x
c) −µk Mtot g∆x
d) − 12 µk Mtot g∆x
2. With what speed is the ball launched from the spring? (This occurs at the moment the
spring is at the equilibrium position; at this point, the spring stops, and the ball loses
contact with the spring.)
a) 20.0 m/s
b) 12.2 m/s
c) 10.0 m/s
d) 8.7 m/s
e) 6.0 m/s
5. If the ball rebounds elastically with the ground, what angle, θ, does the ball’s velocity
vector make with the horizontal immediately after leaving the ground?
a) 42.1o
b) 49.2o
c) 52.3o
d) 54.4o
e) 56.5o
3. The ball now slides along the frictionless track, and by the time it arrives at the bottom
of the first valley, it has a speed vb = 20.0 m/s. At this point, the cross-sectional shape
of the valley may be approximated by a circle of radius R = 7.50 meters. What is the
magnitude of the normal for exerted on the ball when it is at the bottom of the track?
(assume that the ball is a point mass for this problem; i.e. assume the radius of the
ball is zero)
a) 4.9 N
b) 9.8 N
c) 16.7 N
d) 29.2 N
e) 31.6 N
6. Now the ball collides with a stationary block of mass M = 1.5 kg. The ball impacts
the block with speed vc = 8.966 m/s. If the collision is completely inelastic (so that the
ball sticks to the block), what is the velocity of the system after the collision?
a) 1.23 m/s
b) 2.24 m/s
c) 3.60 m/s
d) 3.68 m/s
e) none of these
8. Suppose that the 2.00 kg object exits the rough patch with a speed of 1.0 m/s and
then impacts and sticks to an initially uncompressed spring with spring constant
k2 = 5.00 N/m. What will be the amplitude of the resulting simple harmonic motion?
a) 0.22 m
b) 0.63 m
c) 0.87 m
d) 0.92 m
e) 1.24 m
9. For the previous question, what will be the period of the simple harmonic motion?
a) 1.82 s
b) 2.07 s
c) 3.25 s
d) 3.97 s
e) 4.81 s
f) none of these