Elastic Force

Elastic restoring forces in springs and deformable bodies governed by Hooke's law.

General idea of the topic

The elastic force is the force exerted by a spring, a rubber band, or any deformable body when it is stretched or compressed from its natural position. For small deformations it is proportional to the elongation and always points toward the equilibrium position, which is why it is called a restoring force.

This topic introduces Hooke's law, the spring constant as a measure of stiffness, and systems of several springs, where the equivalent constant depends on whether they are arranged in series or in parallel. It also states its limit: beyond a certain stretch the material stops being elastic and proportionality is lost.

What the student is expected to understand

By the end, the student should know how to calculate the force of a spring from its deformation, interpret the sign of the force relative to the direction of the deformation, and find the equilibrium position of a body hanging from a spring.

The student should also be able to combine springs in series and in parallel and recognise when Hooke's law stops being valid.

Recommended learning route

1. Hooke's law: states the proportionality between force and deformation, defines the spring constant, and studies its sign and its limits.
2. Spring systems: combines several springs, calculates the equivalent constant, and solves the equilibrium of bodies attached to them.

Physical criterion to acquire

The essential criterion is always to measure the deformation from the natural length of the spring, not from its total length, and to give the force the direction that tends to restore that length. Mixing up the origin of the deformation or its sign leads to errors in the magnitude and in the direction of the force.

Connection with real problems

• spring scales and dynamometers.
• vehicle suspensions and shock absorbers.
• mattresses, trampolines, and return mechanisms.
• materials: stiffness and elastic limit.

Goal of the topic

The final goal is to apply Hooke's law to single and combined springs, calculate forces and equilibrium positions, and recognise its range of validity.