#### 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*