1. 6 Work and Kinetic Energy Work Done by a Constant Force Work Done by a Variable Force – Straight Line Motion The Scalar Product Work-Kinetic Energy Theorem – Curved Paths Hk: 27, 41, 49, 51.

2. Energy: The work that a physical system is capable of doing in changing from its actual state to a specified reference state … (American Heritage Dictionary) Energy: The capacity to do work. (Physics) What is Work? Some Definitions

3. Work Transformation Work is a usage of energy, e.g., Burning gasoline produces heat & motion battery running a car /

4. Work Work is force x distance (N·m = joule), force parallel to motion (no work done by perpendicular component) It takes energy to do work. Less stored energy is available after productive work is done.

5. Work by Constant Force Work = Fcos  x = (80N)(cos40)(11m) = 674 J Ex: F = 80N, Angle is 40°,  x is 11m,

6. Total Work on Object

7. Kinetic Energy

8. Example: 20kg moving at 5m/s. 250J of work (total) are done on it. What is its final speed?

9. Negative Work (object slows down) Ex. A car moves 10 meters while a braking force of 500 newtons acts.

10. Ex. Block pushed 3m with 75N of force while Friction of 50N. Total Work is,

11. Work by a Variable Force, Straight Line Motion

12. Hooke’s Law Elastic restoring force proportional to deformation F = -kx k = elastic constant (N/m) Ex. Lab springs, k = 8N/m, 0.1kg mass: mg = kx (0.1kg)(9.8N/kg) = 8N/m(x) x = 0.98N/(8N/m) = 0.1225 m

13. Scalar (Dot) Product

14. Ex: A = (1, 1, 0), B = (5, 0, 0)

15. Example: Find the angle between A = (1, 1, 1) and B = (5, 0, 0)

17. Power

18. Ex: A car drives at 20m/s and experiences air-drag of 400N.

19. What size motor needed when Operating Speed is 10cm/s? Cube of bricks ~ 1 ton 1 ton = 2000 lbs ~ 9000 N Minimum Power: P = Fv = (9000N)(0.1m/s) P = 900 W = 1.2 hp

20. Work along Curved Path

21. Summary Work is force parallel to path x distance (force constant) Negative total work (object slows down) Work is integral of force·distance (Scalar Product) Power is rate work is done Total work = change in KE /