Work Done by a Varying Force

So far...

Forces are constantWork done = F·s

Consider...

• Force on the spring varies as the length increases

• As the spring is displaced the force varies

Let’s look at the graph

• Area under the graph = F·s

• Area under the graph = Work done

Let’s look at the graph

• Area under the graph = Work done

• Work done to stretch a spring = ½ Fx

Spring Extension

• Force is proportional to extension

• Slope of the graph is constant

• Slope = Spring constant– a.k.a. force constant

• Equation

Strain Energy

• Stored energy due to stretching or compression

• Work-Energy Theorem• Work done on the spring• Work done by the spring

Example

Example

Example

Example

Example