   Chapter 7, Problem 5CQ

Chapter
Section
Textbook Problem

A pendulum consists of a small object called a bob hanging from a light cord of fixed length, with the top end of the cord fixed, as represented in Figure CQ7.5. The bob moves without friction, swinging equally high on both sides. It moves from its turning point A through point B and reaches its maximum speed at point C. (a) At what point does the bob have non-zero radial acceleration and zero tangential acceleration? What is the direction of its total acceleration at this point? (b) At what point does the bob have nonzero tangential acceleration and zero radial acceleration? What is the direction of its total acceleration at this point? (c) At what point does the bob have both nonzero tangential and radial acceleration? What is the direction of its total acceleration at this point? Figure CQ7.5

a)

To determine
The point where the bob will have non-zero radial acceleration and zero tangential acceleration.

Explanation

Given info: The maximum displacement of the pendulum occurs at point A . From A the pendulum passes through the point B and reaches the point C where the speed of the pendulum is maximum.

Explanation:

The centripetal or radial acceleration of a particle is given by,

ac=v2r

• v is the linear velocity of the pendulum
• r is the radius

The tangential acceleration of a particle is given by,

at=rα

b)

To determine
The point where the bob will have zero radial acceleration and non-zero tangential acceleration.

c)

To determine
The point where the bob will have non-zero radial acceleration and non-zero tangential acceleration and the direction of the total acceleration at this point.

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