Question

A $40mm$ long spring is stretched by applying a force. If $10N$ force is required to stretch the spring through one mm, then work done in stretching the spring through $40mm$ is:

Answer 1

Step 1: Given data

Length of the spring (L) = $40mm$

Force (F) applied to stretch the spring by one mm ($0.001m$) = $10N$

Step 2: Formula used

1. $F=kx$, where F is the force applied to stretch the spring, k is the spring constant and x is the displacement.
2. $W=\frac{1}{2}k{x}^2$, where W is the work done to deform the spring.

Step 3: Find the spring constant

Hooke's law states that:

$F=kx$

On substituting the given values in the formula, we get:

$$\begin{gathered} 10=k\times {10}^{-3} \\ \Rightarrow k={10}^{4}N/m \end{gathered}$$

Step 4: Calculate work done

The formula for work done in stretching a spring is:

$W=\frac{1}{2}k{x}^2$

It is given that $x=40mm=0.04m$.

On substituting the given values in the formula, we get:

$$\begin{gathered} W=\frac{1}{2}\times {10}^4\times {\left(0.04\right)}^2 \\ W=8J \end{gathered}$$

Thus, the work done in stretching the spring through $40mm$ is $8J$.