   Chapter 5.4, Problem 10E

Chapter
Section
Textbook Problem

# If the work required to stretch a spring 1 ft beyond its natural length is 12 ft-lb, how much work is needed to stretch it 9 in. beyond its natural length?

To determine

To find:

The work needed to stretch the spring 9 in. beyond its natural length

Explanation

1) Concept:

Use Hook’s law and formula of work done

2) Law and Formula:

Hook’s law:

The force required to stretch a spring  x units beyond its natural length is proportional to x, and it is given by fx=kx where k is a positive constant called the spring constant.

Work done:

W=abf(x)dx

3) Calculation:

From the given information,

12=01kxdx

Simplify,

12=kx2201

12=k(1)22-k(0)22

12=k2

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