Elastic Potential Energy
- When a spring is stretched or compressed by a force, work is done by the spring
- Work done is the transfer of energy
- The energy is transferred to its elastic potential energy store
When a spring is stretched or compressed, there is work done and elastic potential energy is stored
- Elastic potential energy is defined as:
The energy stored in an elastic object when work is done on the object
- Provided the spring is not inelastically distorted (i.e has not exceeded its limit of proportionality), the work done on the spring and its elastic potential energy stored are equal
- The work done, or the elastic potential energy stored, while stretching or compressing a spring can be calculated using the equation:
E = ½ kx2
- Where:
- E = elastic potential energy (energy transferred in stretching) in joules (J)
- k = spring constant in newtons per metre (N/m)
- x = extension in metres (m)
The elastic potential energy in a stretched spring depends on its spring constant and extension
- This equation is only for springs that have not been stretched beyond their limit of proportionality
- The term x2 means that if the extension is doubled then the work done is quadrupled
- This is because 22 = 4
Worked example
A mass is attached to the bottom of a hanging spring with a spring constant k and 0.2 J of work is done to stretch it by 4.5 cm.Calculate the spring constant, k for this spring.
Examiner Tip
Remember: when calculating the work done the extension, x, is squared (x2)!
