# A uniform ball of radius R rolls without slipping between two rails such that the horizontal distance is d between

## Question:

(a) In a sketch, show that at any instant Vcm = CdYR2 - d 2/4. Discuss this expression in the limits d = 0 and d = 2R.

(b) For a uniform ball starting from rest and descending a vertical distance h while rolling without slipping down a ramp, Vcm = Y IOgh/7 €¢ Replacing the ramp with the two rails, show that

In each case, the work done by friction bas been ignored.

(c) Which speed in part (b) is smaller? Why? Answer in terms of how the loss of potential energy is shared between the gain in translational and rotational kinetic energies.

(d) For which value of the ratio d/ R do the two expressions for the speed in part (b) differ by 5.0% by 0.50%?

## This problem has been solved!

Do you need an answer to a question different from the above? Ask your question!

## Step by Step Answer:

**Related Book For**

## Vector Mechanics for Engineers Statics and Dynamics

**ISBN:** 978-0073212227

8th Edition

**Authors:** Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell

**View Solution**

Create a free account to access the answer

**Cannot find your solution?**

Post a FREE question now and get an answer within minutes.
* Average response time.