Elastic Potential Energy (DP IB Physics: HL): Revision Note

Elastic Potential Energy

• Elastic potential energy is defined as

The energy stored within a material (e.g. in a spring) when it is stretched or compressed

• Therefore, for a material obeying Hooke’s Law, elastic potential energy is equal to:

$E_H=\frac{1}{2}k∆x^2$

• Where:

  • k = spring constant of the spring (N m^–1)

  • Δx = extension of the spring (m)

• This can also be written as:

$E_H=\frac{1}{2}F∆x$

• Where:

  • F = restoring force (N)

• This force is the same restoring force as in Hooke's law: $F=k∆x$

A spring that is stretched or compressed has elastic potential energy

• It is very dangerous if a wire under large stress suddenly breaks

• This is because the elastic potential energy of the strained wire is converted into kinetic energy

$E_H=E_K$ 

$\frac{1}{2}k∆x^2=\frac{1}{2}m{v}^2$

$v\propto ∆x$

• This equation shows

  • The greater the extension of a wire Δx the greater the speed v it will have when it breaks