1. APHY201 2/22/2016 1 6.5 Conservative and Non-conservative Forces   Path dependant or path independent?   W net = W C + W NC where W NC = ΔKE + ΔPE

2. APHY201 2/22/2016 2 6.6 Conservation of Mechanical Energy   If only conservative forces act within a system then the total mechanical energy of the system is constant. ΔKE + ΔPE = 0 ½ mv 1 2 + mgy 1 = ½ mv 2 2 + mgy 2 (PE grav only) ½ mv 1 2 + ½ kx 1 2 = ½ mv 2 2 + ½ kx 2 2 (PE spring only)

3. APHY201 2/22/2016 3 6.10 Power   The rate at which work is done   Unit: watts (J/s) 1 hp = 746 watts   Energy consumption: 1 kilowatt-hour = 3.6 x 10 6 J

4. APHY201 2/22/2016 4 6.10 Power

5. APHY201 2/22/2016 5 6.10 Power

6. APHY201 2/22/2016 6 Machines   They multiply forces, not energy !!!   Work input < Work output → Why?   Lever, screw, inclined plane, pulley, wheel and axle, wedge.

7. APHY201 2/22/2016 7 Machines

8. APHY201 2/22/2016 8 Machines

9. APHY201 2/22/2016 9 In class: Problems 35 and 78 (a,b) Other problems ↓ 38. Use conservation of energy. Subscript 1 represents the projectile at the launch point, and subscript 2 represents the projectile as it reaches the ground. The ground is the zero location for PE. Note that the angle of launch does not enter into the problem.

10. APHY201 2/22/2016 10 52. Since the crate moves along the floor, there is no change in gravitational PE. Note that the two forces doing work do work over different distances.