(a) What is the smallest value of h that will work?
(b) Suppose that I make h = 6 R. What is the normal force of the track on the ball at the lowest point?
1. Write out your solution for #2. CLPhys1 11.P.055 on the WebAssign
Problem Set 2.0 dynamics/rolling 043.
| 2. A small solid marble of mass m and radius r rolls
without slipping along a track shown. The marble is released from rest at
a height h, and we want the ball to make it around the loop, radius R >>
r. (This is similar to problem 6 in Chapter 8, but now we add the rotation
of the ball.) Answer in terms of m, r, R, and g —not all of these may
appear. (a) What is the smallest value of h that will work? (b) Suppose that I make h = 6 R. What is the normal force of the track on the ball at the lowest point? |
|
(c) Suppose I release the ball from too low a height and it does not complete the loop. Describe the motion of the ball after it leaves the track. (Give the name of the path or make a sketch.)
| 3. A solid cylinder of mass M and radius R moves along a horizontal table, rolling without slipping on a frictionless axle. The axle of the cylinder is attached to a spring of spring constant k, as shown. The cylinder is pulled to the right so that the spring is initially stretched an amount X, and released from rest. Find the speed of the cylinder when it returns to the point where the spring is relaxed. The answer should contain only these symbols: k, X, M, and R, and any constants like g. (Not all of these may appear.) |  |
This page maintained by Anne G. Young. Last modified 24-Mar-2005 .