How is the work done in stretching a wire related to elastic potential energy?

The work done in stretching a wire is related to the elastic potential energy stored in the wire.

When a force is applied to stretch a wire, work is done against the restoring force of the wire. This work is stored as elastic potential energy in the wire, which is the energy that is stored in an object when it is deformed and can be recovered when the object returns to its original shape.

The amount of elastic potential energy stored in a wire is directly proportional to the amount of work done in stretching it. This can be expressed mathematically as:

Elastic potential energy = 1/2 kx^2

Where k is the spring constant of the wire and x is the amount by which the wire is stretched.

The relationship between the work done and the elastic potential energy stored in a wire can be seen in the graph of force against extension. The area under the graph represents the work done in stretching the wire, and this is equal to the elastic potential energy stored in the wire.

In summary, the work done in stretching a wire is related to the elastic potential energy stored in the wire. The more work done in stretching the wire, the more elastic potential energy is stored in it.