TAP 305- 3: Elastic energy
The relationship between force to extend a spring, and extension, determines the energy
stored.
Energy stored in a stretched spring
area below graph
= sum of force 
change in displacement
extra area
F1 x
F1
total area
1 Fx
2
0
x
0
unstretched
extension x
force F1
work F1 x
no force
larger force
Energy supplied
small change x
energy supplied = F x
F=0
x=0
F = kx
x
stretched to extension x by force F:
energy supplied = 12 Fx
spring obeys
Hooke’s law: F = kx
energy stored in stretched
spring = 12 kx2
Energy stored in stretched spring is 12 kx2
Practical advice
This diagram is reproduced here so that you can talk through it, or adapt it to your own
purposes.
External reference
This activity is taken from Advancing Physics chapter 10, 120 O