Force-Extension Graphs & Elastic Potential Energy

What does a straight line through the origin show on a force–extension graph?

Force and extension are directly proportional.

What does a curved section of a force–extension graph show?

The relationship is non-linear, so Hooke's law no longer applies.

What does the gradient of a force-against-extension graph represent?

The spring constant.

What does a steeper gradient indicate?

A larger spring constant, meaning a stiffer spring.

How can you identify the limit of proportionality on a graph?

It is the point where the graph stops being a straight line through the origin.

Why should a line of best fit be used?

To represent the overall trend in the data and reduce the effect of random errors.

What happens when a spring is stretched?

Work is done on the spring, transferring energy to its elastic potential energy store.

When does the usual elastic potential energy equation apply?

When the spring obeys Hooke's law, up to its limit of proportionality.

What is the relationship between work done and elastic potential energy?

If losses are negligible and deformation is elastic, the work done stretching the spring equals the elastic potential energy stored.

What happens to elastic potential energy if extension doubles?

It becomes four times larger, provided the spring constant remains constant and Hooke's law applies.