Instructions:
Test is 2hours long. Do five problems, your choice. Staple and sign test when finished.Be neat and show all work including units! You get credit for doing this!
Problem 1:
A pole vaulter jumps over a bar of height 5.8 m and falls back to the ground. The total change in the vaulter's gravitational potential energy during the fall is - 3.70x 103 J. What is his weight?
Problem 2:
A car of mass m1 traveling at speed v1 collides with the back of a truck of mass 2m2 traveling with speed v2< v1. Their bumpers lock together.
a) What is the speed of the coupled vehicles immediately after the collision?
b) What is the change in kinetic energy of the car-truck system in this collision?
c) Where did the kinetic energy go?
Problem 3:
Three particles are located in the x-y plane as follows: 3 kg at (2 m, 5 m), 4 kg at (-1 m, -1 m) and 2 kg at (3 m, -2 m). Calculate
a) their center of mass, and
b) their total moment of inertia about the z-axis.
Problem 4:
A disk of mass 30.0 kg and diameter 0.300 m is mounted on a horizontal frictionless rotation axis. A massless, stretchless rope is wrapped around the circumference of the disk and a weight of mass 1.4 kg is hung from the end of the rope vertically over a pulley. As the weight falls, the disk turns.
a) Assuming the rope does not slip on the disk and the disk starts from rest, what is the angular velocity of the disk when the mass has fallen 0.75 m?
b) What is the angular momentum of the disk-mass system?
Problem 5:
A race car travels on a circular track of radius 250 m. Assuming the car moves with a constant speed of 45.0 m/s, find its
a) angular speed, and
b) the magnitude and direction of its acceleration.
Problem 6:
A rod of length L and mass 5 kg is lying on a frictionless table and is constrained to rotate about one end. A particle of mass 1 kg traveling at 1.5 m/s perpendicular to the rod hits and sticks to the other end of the rod.
a) What is the angular velocity of the mass-rod system after the collision?
b) What is the change in the kinetic energy of the mass-rod system?
c) Where did the kinetic energy go?