How do you calculate work done in stretching a spring?

To calculate work done in stretching a spring, use the formula: Work = 0.5 × k × x².

When you stretch a spring, you are doing work against the spring's restoring force. This work can be calculated using the formula: Work = 0.5 × k × x², where 'k' is the spring constant and 'x' is the extension (or compression) of the spring from its natural length.

The spring constant 'k' is a measure of the stiffness of the spring. It tells you how much force is needed to stretch or compress the spring by a unit length. The unit of the spring constant is Newtons per metre (N/m). You can find the spring constant by performing an experiment where you measure the force applied to the spring and the corresponding extension, then use Hooke's Law (F = kx) to calculate 'k'.

The extension 'x' is the amount by which the spring is stretched or compressed from its equilibrium position. It is measured in metres (m). If you stretch a spring by 0.1 metres, then 'x' would be 0.1.

The formula Work = 0.5 × k × x² comes from the fact that the force needed to stretch a spring increases linearly with the extension. This means that the work done is not simply force times distance, but rather the area under the force-extension graph, which is a triangle. The factor of 0.5 accounts for this triangular area.

For example, if you have a spring with a spring constant of 200 N/m and you stretch it by 0.05 metres, the work done would be: Work = 0.5 × 200 × (0.05)² = 0.5 × 200 × 0.0025 = 0.25 Joules. This means you have done 0.25 Joules of work to stretch the spring.