Directions: All questions have equal value. Do not spend too much time on any one problem. Do everything that you can do easily, and then return to parts that are harder for you. If you cannot answer one part of a question that you need for a later part then assume an answer or use a symbol to represent the part that you do not know.
Useful number(s): Gravitational Constant: G=6.6726x10-11 N×m2/kg2
1) A puck of mass M = 0.4 kg is sliding on a frictionless surface at a speed V=2.50 m/s in the x-direction and hits another puck of mass m = 0.2 kg at rest at the origin. The collision lasts 0.003s. The smaller mass leaves the collision at an angle of 35 degrees above x-axis and the larger at an angle of 40 degrees below the x-axis.
a) What are the final speeds of the particles?
b) What is the total change in kinetic energy during the collision?
c) Is the collision elastic?
d) What is the impulse applied to the smaller particle during the collision?
e) What is the average force?
2) A 50kg coyote named Wile E. is trying to catch The Road Runner (a small bird). Wile E. climbs to the top of a 100m cliff. The Road Runner is at the base of the cliff. Wile E. drops a 2kg rock from rest attached to a massless rope off of the cliff.
a) Assuming the potential energy of the rock is zero on the ground, what is the potential energy when the rock is released 100m above the ground?
b) What is the initial kinetic energy of the rock?
c) How fast is the rock traveling when the rock has fallen half way down.
d) When the rock is half way down the rope attached to it gets stuck around Wile E’s leg and Wile E. falls off of the cliff as well. What is the speed of the rock (and Wile E since he is attached) when the rock hits the ground?
e) What is the speed of Wile E when he hits the ground?
3) A bicycle with wheels of 0.5m radius is traveling over a circular hill of radius 30m at a constant speed of 5m/s.
a) What is the Normal force on the bicycle at the top of the hill?
b) What is the Normal force at an angle of 30 degrees shown in the figure?
c) When the bicycle has traveled through a distance of 10m (as measured at the center of the tires) how many revolutions have the tires gone?
d) What is the angular velocity of the bicycle?
e) What is the angular velocity of the bicycle wheel?
f) What is the angular acceleration of the bicycle?
g) What is the tangential acceleration of the bicycle?
4) A slingshot (a rock attached to a string) of radius 1m. The rock starts at rest. After 3 revolutions under a constant angular acceleration the rock is moving at 5m/s.
a) What is the angular velocity?
b) What is the angular acceleration?
c) How long did the 3 revolutions take?
d) What is the average angular speed?
e) What is the total acceleration vector of the rock?