# Sample Midterm I

```Physics 135-1 Midterm, Spring 2014
Show all work for partial credit
Name ________________________________
1) (10 points) Suppose a ferris wheel with a radius of
3.5 meters is rotating clockwise at a rate of 5 revolutions
per minute. The bottom of the wheel is elevated 1.75 m
above the ground, as shown. Then, just as she reaches the
very top of the wheel, a lady accidently drops her teddy
bear. At what horizontal distance from the center of the
wheel will the teddy bear hit the ground?
2) Two people are pulling on a barge in a river with ropes.
One is pulling at 34° south of horizontal, and the other is
pulling at 45° north of horizontal. The barge itself is
moving only along the x-axis (horizontal). It has a mass of
200 kg.
2a) (5 points) If the barge is resisting their pull with
180 N of frictional force, and is gently accelerating at
0.2 m/s2, what is the tension in the north and south ropes?
2b) (5 points) Assuming the barge starts at rest, how much work (in joules) will the two people
have expended after pulling on it for one minute in this way?
3a) (6 points) A rock A of mass 1 kg is
moving at 40 m/s along the positive x-axis.
Then it collides with another rock B of equal
mass and ricochets away at a positive 30°
relative to the x-axis. The second rock B
moves away at a negative 45° relative to the
x-axis. How fast is each rock moving after the
collision?
3b) (4 points) How much heat is generated by this collision?
4) (10 points) A sphere of mass M = 5 kg and
radius R = 40 cm has a cord tied around its
equator, which is also attached to a small mass
of m = 1.5 kg. The system is originally at rest.
Then the small mass is released and allowed to
fall. After it has fallen 50 cm, how fast (in
radians per second) will the sphere be rotating?
There is no friction in the system, and the
pulley has no mass.
5) Assume that a frictionless cart of mass 4m is at the
origin on a one-dimensional track. Assume that
another cart of mass 2m is at x = 1 m and a third cart
of mass m is at x = 2 m. The first cart is moving at
v0 = 3 m/s; the other two carts are initially motionless.
5a) (5 points) Where is the center of mass of this system at t = 0?
5b) (5 points) Assume that the first cart collides with and sticks to the second cart, and then the
second cart collides with and sticks to the third cart. Where is the center of mass of this system at
t = 5 sec?
```