2. Work done by a variable force

3. A graphical view of Work = Force x Distance
Of course, this force isn’t varying….

4. We can approximate a varying force with a series of constant forces

5. We can approximate a varying force with a series of constant forces
We get a better approximation if we use more segments of shorter duration

6. We can approximate a varying force with a series of constant forces
We get a better approximation if we use more segments of shorter duration
Bottom line: The work done by a varying force is the area under the force vs. position curve

7. So back to the spring example…

8. So back to the spring example…
The “area under the curve” is the area of this triangle
The area of a triangle is ½ base · height

9. So back to the spring example…
The “area under the curve” is the area of this triangle

10. Example:
The spring in a child’s toy has a force constant (also called a “spring constant”) of 295 N/m. How much work is required to stretch this spring 1.75 cm?

11. Example:
The spring in the suspension of a car has a spring constant k = 23,400 N/m. If J of work is done on this spring, how far is it compressed?

12. “Springs” in other contexts

13. “Springs” in other contexts
AFM image of an integrated circuit
Atomic Force Microscope
AFM image of human chromosomes

14. The work required to deflect a typical AFM cantilever by 0. 10 nm is 1
The work required to deflect a typical AFM cantilever by 0.10 nm is 1.2 x J.
(a) What is the force constant of the cantilever, treating it as an ideal spring?

15. The work required to deflect a typical AFM cantilever by 0. 10 nm is 1
The work required to deflect a typical AFM cantilever by 0.10 nm is 1.2 x J.
(a) What is the force constant of the cantilever, treating it as an ideal spring?
(b) How much work is required to increase the deflection of the cantilever from 0.10 nm to 0.20 nm?

16. The work done by a spring can be either positive or negative…

17. Example:
A block with a mass of 1.5 kg and an initial speed of 2.2 m/s slides on a frictionless, horizontal surface. The block comes into contact with a spring that is in its equilibrium position and compresses it until the block comes momentarily to rest. Find the maximum compression of the spring, assuming it force constant is 475 N/m.