   Chapter 7, Problem 51AP

Chapter
Section
Textbook Problem

An athlete swings a 5.00-kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.800 m at an angular speed of 0.500 rev/s. What are (a) the tangential speed of the ball and (b) its centripetal acceleration? (c) If the maximum tension the rope can withstand before breaking is 100. N, what is the maximum tangential speed the ball can have?

(a)

To determine
The tangential speed of the ball.

Explanation

Given info: The mass of the ball is 5.00kg . The radius of the circle in which the ball rotates is 0.800m . The angular speed of the ball is 0.500revs-1 .

Explanation:

The tangential velocity of the ball is given by,

v=rω

• r is the radius of the ball
• ω is the angular speed

Substitute 0.500revs-1 for ω , 0.800m for r to determine the linear velocity of the ball,

v=(0.800m)(0

(b)

To determine
The centripetal acceleration of the ball.

c)

To determine
The maximum tangential speed the ball can withstand before breaking down.

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