Chapter 5.4, Problem 9E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 42 cm.

(a) How much work is needed to stretch the spring from 35 cm to 40 cm?

(b) How far beyond its natural length will a force of 30 N keep the spring stretched?

To determine

**(a)**

**To find:**

The work needed to stretch the spring from to

Explanation

**1) Concept:**

Use Hookâ€™s law and formula of work done

**2) Law and Formula:**

Hookâ€™s law:

The force required to maintain a spring stretched units beyond its natural length is proportional to

Work done:

**3) Calculation:**

a) According to Hookâ€™s law, the force required to hold the spring stretched meters beyond its natural length is

From the given information, of work is needed to stretch a spring from its natural length of

Therefore, the amount of stretched is

Thus,

Simplify,

To determine

**b)**

**To find:**

How far beyond its natural length will a force of keep the spring stretched?

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