1. Kinetic Energy work of changing speed § 6.2

2. Rebounding Ball What is the sign of the work done on the ball by the wall as it slows (squishes)? A.Positive (W > 0). B.Negative (W < 0). C.Zero (W = 0). D.Can’t tell (W = ?).

3. Rebounding Ball What is the sign of the work done on the ball by the wall as it rebounds (expands)? A.Positive (W > 0). B.Negative (W < 0). C.Zero (W = 0). D.Can’t tell (W = ?).

4. Happy/Sad Balls Which ball has the greatest change in kinetic energy  K during impact? A.The happy (rebounding) ball. B.The sad (dead) ball. C.Both had the same  K.

5. Happy/Sad Balls Which ball has the most (largest absolute value) work done on it during impact? A.The happy (rebounding) ball. B.The sad (dead) ball. C.Both had the same W.

6. Work in General changing forces, curving paths § 6.3

7. What’s the point? What is work when force is not constant or the path is not straight?

8. Work in General For constant force, W = F·s. In general, dW = F·ds. So, W =  F·ds. (Sum of work done over each interval.) Path may not be straight. F may vary with position or time.

9. Elastic Force Stretching and squishing still § 6.3

10. Hooke’s Law Formula F = force exerted by the spring k = spring constant; units: N/m; k > 0 x = displacement from equilibrium position negative sign: force opposes distortion F = –kx

11. Work to Deform a Spring Push or pull a distance x from equilibrium x kx force displacement kx 2 1 2 = slope = k area = w Work =F·x ; 1 2 F = kx Work = kx·x 1 2

12. Poll Question A spring with force constant k is stretched from x = 0 to x = D. What is the work done by the spring as it stretches? A.1/2 kD 2. B.–1/2 kD 2. C.0. D.It cannot be determined. E.None of these.

13. Poll Question Two springs, one with a spring constant k 1 and the other with a spring constant k 2 = 2 k 1, are slowly stretched to the same final tension. Which spring has more work done on it? A.The stiffer spring (k = k 2 = 2 k 1 ) B.The softer spring (k = k 1 ) C.The same work was done on both.

14. Centripetal Force work of acceleration § 6.3

15. Group Poll Question A toy of mass m moving at constant speed v in a circle of radius r has a constant magnitude of centripetal acceleration of v 2 /r. Its velocity reverses every half-cycle. How much work does the centripetal force do on the toy every half-cycle? A. mv 2. B. –mv 2. C.  mv 2. D. None of these.

16. Kinetic Energy and Direction K depends on speed Direction of velocity is irrelevant Changing only direction requires force, but no work. 1/2 mv 2 = 1/2 mv  v is a scalar.

17. Net Force and Net Work Net force is nonzero if a body accelerates net work is nonzero if a body changes speed The net force must overlap with the displacement to do work!