1. Energy Conservation And Non-Conservative Forces

2. Conservation of Mechanical Energy Definition of mechanical energy: (8-6) Using this definition and considering only conservative forces, we find Or equivalently

3. Conservation of Mechanical Energy Energy conservation can make kinematics problems much easier to solve

4. Catching a Home Run At the bottom of the 9 th inning, a player hits a 0.15 kg baseball over the outfield fence. The ball leaves the bat with a speed of 36.0 m/s and a fan in the bleachers catches it 7.2 m above the point where it was hit. Neglect air resistance. (a) What is the kinetic energy K f of the ball when caught? (b) What is the speed v f of the ball when caught.

5. Speed and Path Energy is a scalar. The speed of the cap is v i at height y i and its speed is v f at height y f, independent of the path between the two heights. Thus the angle at which the cap is launched does not change this result, as long as v i is large enough to carry the cap to height y f.

6. Energy of a Ball ACT 2m m h When a ball of mass m is dropped from height h, its kinetic energy just before landing is K. If a 2 nd ball of mass 2m is dropped from height h/2, what is its kinetic energy just before landing? (a) K/4 (b) K/2 (c) K (d) 2K (e) 4K

7. Non-conservative Forces In the presence of non-conservative forces, the work done by these forces must be included in the energy calculations. This term is equal to the energy expended in overcoming the non-conservative force (usually friction) or to the energy gained from work done by the non-conservative force. E nc = -W nc

8. Skiing w/ Friction A 50 kg skier goes down a 78 meter high hill with a variety of slopes. She finally stops at the bottom of the hill. If friction is the force responsible for her stopping, how much work does it do? Similar to bob sled homework 0 0 0

9. Galileo’s Pendulum ACT How high will the pendulum swing on the other side now? A) h 1 > h 2 B) h 1 = h 2 C) h 1 < h 2 h1h1 h2h2 m Conservation of Energy (W nc =0) K initial + U initial = K final +U final 0 + mgh 1 = 0 + mgh 2 h 1 = h 2 44

10. Find the Diver’s Depth A 95.0 kg diver steps off a diving board and drops into the water, 3.00 m below. At some depth d below the water’s surface, the diver comes to rest. If the non-conservative work done on the diver is W nc = -5,120 J, what is the depth d? 0 of U 0 0

11. Judging a Putt A golfer badly misjudges a putt, giving the ball an initial speed v 1, which sends the ball a distance d that is only one quarter of the distance to the hole. If the non-conservative force f due to the resistance of the grass is constant, what initial speed v 2 would have been needed to putt the ball from its initial position to the hole? 1

12. Landing with a Thud A block of mass m 1 = 2.40 kg is on a horizontal table with a coefficient of friction  k = 0.450 between them and is connected to a hanging block of mass m 2 = 1.80 kg as shown. When the blocks are released, they move a distance d = 0.50 m, and then m 2 hits the floor. Find the speed of the blocks just before m 2 hits.

13. Potential Energy Curves and Equipotentials The curve of a hill or a roller coaster is itself essentially a plot of the gravitational potential energy:

14. Potential Energy Curves The potential energy curve for a mass and spring Total mechanical energy