Chapter 6, Problem 28P

To determine

Additional work required to stretch the spring by 4cm.

Answer to Problem 28P

Solution:Additional 48 J work is required to stretch the spring by 4cm if it takes 6 J of work to stretch spring by 2 cm initially.

Explanation of Solution

Given: Spring is stretched to 2 cm, i.e., $x=0.02\text{ m}$

Work done $=6\text{ J}$

Formula Used:

The work done in spring is given by

  $W=\frac{k{x}^2}{2}$

Where, k is the spring constant.

x is the stretched length of the spring.

Calculations: First, we will find the spring constant using the equation

  $\begin{array}{l}k=\frac{2W}{x^2}\\ k=\frac{2\times 6}{{0.02}^2}\\ k=30000\text{ N/m}\end{array}$

The spring constant of spring is 30000 N/m.

Now find the work required to stretch additional 4 cm.

  $\begin{array}{l}W=\frac{k{x}^2}{2}\\ W=\frac{30000{(0.02+0.04)}^2}{2}\\ W=54\text{ J}\end{array}$

The additional work is $54-6=4\text{8 J}$ .

Conclusion:Additional 48 J work is required to stretch the spring by 4cm if it takes 6 J of work to stretch spring by 2 cm initially.