Stretching & Compressing using Force

Elastic deformation: the object returns to the original shape & size when the force is removed

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Inelastic Deformation: The object is changed permanently when the force is removed

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Hooke’s Law:

The extension of an elastic object, such as a spring, is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.

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Some springs are easy to stretch. They have a low spring constant (unit: N/m)

Some springs are difficult to stretch. They have a high spring constant .

To find the force needed to stretch (or compress) a spring:

force = spring constant × extension

This relationship also applies to the compression of an elastic object, where ‘extensions’ would be the compression of the object.

force = spring constant × extension

3.0 = spring constant x 0.12

spring constant = 3.0 / 0.12

The spring constant is 25 N/m

remove the mass

if the spring returns to the original length it is behaving elastically

A force that stretches (or compresses) a spring does work and elastic potential energy is stored in the spring. Provided the spring is not inelastically deformed, the work done on the spring and the elastic potential energy stored are equal.

On a graph of force on the y-axis and extension of the x-axis:

  • The gradient = spring constant
  • The area under the graph = work done to stretch/compress the spring
Force-Extension Graph for a Spring

Calculate work done in stretching (or compressing) a spring (up to the limit of proportionality) using the equation:

elastic potential energy = 0.5 × spring constant × extension²

  •  work done is equal to elastic potential energy
  • as long as the spring does not go past the limit of proportionality

elastic potential energy = 0.5 × spring constant × extension²

elastic potential energy = 0.5 x 13.5 x 0.122

the elastic potential energy is 0.097 Joules

the student measured / recorded the length of the spring (and not extension)

so extension does not equal zero when force = 0