Elasticity and Hooke's lawIB MYP Physics: Revision notes

When you apply a force to a spring or wire, it stretches. The extension is how much longer it becomes:

extension = stretched length − natural (original) length

Example: a spring of natural length 20 cm is 26 cm long under a load. Its extension is 26 − 20 = 6 cm.

Always use the extension, not the whole length, in calculations.

For a spring, the extension is directly proportional to the force applied, as long as the spring is not stretched too far.

F = k x

• F is the force in newtons (N)
• k is the spring constant in N/m (a stiffer spring has a larger k)
• x is the extension in metres (m)

Worked example: a spring extends by 5.0 cm (0.050 m) when a 10 N weight is hung from it. k = F ÷ x = 10 ÷ 0.050 = 200 N/m. A 15 N force would give x = 15 ÷ 200 = 0.075 m = 7.5 cm.

A force-extension graph has force on the vertical axis and extension on the horizontal axis.

• The straight line through the origin shows that extension is proportional to force. Its gradient = k, the spring constant.
• The limit of proportionality is the point where the line starts to curve. Beyond it, Hooke's law no longer works.
• The elastic limit is the largest force the material can take and still return to its original length when the force is removed. It is at or just beyond the limit of proportionality.

The steeper the straight section, the stiffer the spring.

Elastic deformation: the material returns to its original shape and length when the force is removed (a rubber band stretched gently, a spring used within its limit).

Plastic deformation: the material is permanently changed when the force is removed (a spring stretched beyond its elastic limit, a paper clip bent open, modelling clay).

A spring stretched past its elastic limit is weaker and longer afterwards, so it is no longer reliable.

Work is done when you stretch a spring, so energy is stored in it as elastic potential energy. The more you stretch it, the more energy it stores.

When the spring is released, this energy is transferred, for example to kinetic energy of a toy dart or a trampoline user. If a spring is stretched beyond its elastic limit, some of the energy goes into permanently changing the material and is not recovered.