To determine

To find:

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

Answer

6.75 ft· lb

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

⇒k=24 lb/ft

Therefore, the work required to stretch the spring 9 in = ¾ ft is

∫03/424xdx

=24x22034

=24(34)22-24(0)22

=(24)(9)(16)(2)-0

=274

=6.75 ft· lb

Conclusion:

The work needed to stretch the spring 9 in. beyond its natural length is 6.75 ft·lb