1. Work Done by a Varying Force

2. So far...
Forces are constant
Work done = F·s

3. Consider... Force on the spring varies as the length increases
As the spring is displaced the force varies

4. Let’s look at the graph Area under the graph = F·s
Area under the graph = Work done

5. Let’s look at the graph Area under the graph = Work done
Work done to stretch a spring = ½ Fx

6. Spring Extension Force is proportional to extension
Slope of the graph is constant
Slope = Spring constant
a.k.a. force constant
Equation

7. Strain Energy Stored energy due to stretching or compression
Work-Energy Theorem
Work done on the spring
Work done by the spring

8. Example

9. Example

10. Example

11. Example

12. Example