Hooke's Law
By DarthVader
Date: 2023-02-27
Topic: 185 see comments
Post views: 901
Hooke's Law
Hooke's law states that the extension or compression of a spring is proportional to the applied force. The restoring force Fx, produced by the spring as it is stretched, is given by:
Fx = −κx
κ = (kappa) is the spring constant - a measure of how much the spring will extend for a given force - and
Fx = The force in the direction of x (N/m)
Note:
N/m = Newtons per metre, which is a measure of ‘surface tension’, and the base units are: kg/s2
Finding The Energy Stored In A Spring
We can find the energy stored in a spring using Hooke's law and the relationship:
energy = force × displacement
To express a small amount of energy stored, δE, in the form:
δE = Fxδx
Substituting for Fx using Hooke's law:
δE = −κxδx
To find the total energy stored for a given extension, sum all the δE terms to form the integral:
E = − ∫x1x0 κx dx
where x0 and x1 are the initial and final displacements of the spring.
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