next up previous
Next: About this document

Physics 170. Midterm II

Please write your name at the top of the page

There are 4 problems. Each is assigned 25 points.

Problem 1: 25 points

A small point particle of mass 2 kg starts at rest from the top of a hemisphere (radius r=2 m) which is attached to a flat horizontal surface. It begins to slide without friction down the hemisphere. (Hint: Remember the roller coaster example. This problem is the similar in many ways.)

(a) Draw a diagram which shows the forces acting on the particle.

b) At what angle does the particle lose contact with the hemisphere ?

c) What is the velocity of the particle when it loses contact with the hemisphere ?

Problem 2: 25 points

The pendulum on the left is pulled aside to the position shown. It is then released and allowed to collide with the other pendulum which is at rest. After the collision, the two pendula stick together. The two balls have equal masses (m=2 kg).

a) What is the speed of the ball on the left just before the collision ? (give your result in terms of h).

b) How high, in terms of h, does the combination swing ?

Problem 3: 25 points

Astronomers believe that the sun was formed in the gravitational collapse of a dust cloud which filled the space now occupied by the solar system and beyond. Assume that the original dust cloud was a uniform sphere of mass M, radius R and angular velocity tex2html_wrap_inline48 .

a) How fast should the sun be rotating now ? (Assume the sun is a uniform sphere of radius tex2html_wrap_inline50 ). Give your answer in terms of R, tex2html_wrap_inline50 , and tex2html_wrap_inline48 .

Problem 4: 25 points

A rope is wrapped around a 3-kg cylinder of radius 10 cm that is free to turn around an axis through its center. The rope is pulled with a force of 15 N. The cylinder is initially at rest at t=0.

a) Find the torque exerted by the rope. Give both the magnitude and direction of the torque.

b) Find the angular acceleration of the cylinder.




next up previous
Next: About this document

Tom Browder
Wed Sep 3 14:07:57 HST 1997