#### To determine

**To find:**

i) The work done during the compression

ii) The work required to compress the spring to a length of *25 cm*

#### Answer

i) *3 J*

ii) *6.75 J*

#### 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*

Where f(x) is the force function.

**3) Calculation:**

**i)** According to Hook’s law, the force required to hold the spring stretched *x* meters beyond its natural length is *fx=kx*

From the given information the amount compressed is *40-30=10 cm=0.1 m*

The given force is *60 N*

Therefore,

*60=k(0.1)*

*⇒k=600 N/m*

Thus, *fx=600x*

Now, the work required to compress the spring by *0.1 m* is

*W=∫00.1600xdx*

Simplify,

*=600x2200.1*

*=300x200.1*

*=3000.12-02*

*=3000.01-0*

*=3 N.m*

*=3 J*

Therefore,

*W=3 J*

**ii)** The work required to compress the spring to a length of *25 cm=0.15 m* is

*W=∫00.15600xdx*

Simplify,

*=600x2200.15*

*=300x200.15*

*=3000.152-02*

*=3000.0225-0*

*=6.75 N·m*

*=6.75 J*

Therefore,

*W=6.75 J*

**Conclusion:**

i) The work done during the compression is *3 J*

ii) The work required to compress the spring to a length of *25 cm 6.75 J*