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# A uniform ball of radius R rolls without slipping between ISBN: 9780321675460 31

## Solution for problem 100CP Chapter 10

University Physics | 13th Edition

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Problem 100CP

A uniform ball of radius ?R? rolls without slipping between two rails such that the horizontal distance is ?d? between the two contact points of the rails to the ball. (a) In a sketch, show that at any instant . Discuss this expression in the limits ?d? = 0 and ?d? = 2?R?. (b) For a uniform ball starting from rest and descending a vertical distance ?h? while rolling without slipping down a ramp, . Replacing the ramp with the two rails, show that In each case, the work done by friction has 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? d0 the two expressions for the speed in part (b) differ by 5.0%? By 0.50%/?

Step-by-Step Solution:

Solution 100CP Step 1 of 4: a) The distance from the center of the ball to the midpoint of the line joining the points where the ball is in 2 d 2 2 d2 contact with the radius is R ( )2 so v cm = R 4. When d = 0, this reduces to v cm = R, the same as rolling on a flat surface. When d = 2R, the rolling radius approaches zero, and v 0 for any cm Step 2 of 4: b)K = mv + I 1 2 2 2 = [mv 2 + mR ( 2 vcm ) ] 2 cm 5 R (d2) 4 mv 2 = cm[5 + 22 ] 10 (14 R) The conservation of energy of the ball is K = U 2 mvcm[5 + 2 ] = mgh 10 (1 d2) 4 R Now we can find v cm using above relation

Step 3 of 4

Step 4 of 4

##### ISBN: 9780321675460

This full solution covers the following key subjects: ball, rails, show, slipping, speed. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. University Physics was written by and is associated to the ISBN: 9780321675460. Since the solution to 100CP from 10 chapter was answered, more than 281 students have viewed the full step-by-step answer. The answer to “A uniform ball of radius ?R? rolls without slipping between two rails such that the horizontal distance is ?d? between the two contact points of the rails to the ball. (a) In a sketch, show that at any instant . Discuss this expression in the limits ?d? = 0 and ?d? = 2?R?. (b) For a uniform ball starting from rest and descending a vertical distance ?h? while rolling without slipping down a ramp, . Replacing the ramp with the two rails, show that In each case, the work done by friction has 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? d0 the two expressions for the speed in part (b) differ by 5.0%? By 0.50%/?” is broken down into a number of easy to follow steps, and 148 words. This textbook survival guide was created for the textbook: University Physics, edition: 13. The full step-by-step solution to problem: 100CP from chapter: 10 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

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