Conservation of Energy

1. Conservation of Energy Physics

2. Example: Picture • Bob goes bungee jumping off of a cliff. Draw a energy bar graph for the top, middle, and bottom of the jump. Top Middle Bottom

3. When drawing an energy bar graph: • Always start with four boxes TOP Ug Ue K I Etot Etot = mghtower

4. Middle: There is really Internal Energy and the graph would look like this: But on the bar graphs we are going to ignore internal energy and draw the graph like this: MIDDLE Ug Ue K I Etot Etot = mghmid + ½ mv2

5. Bottom: There is really Internal Energy and the graph would look like this: But on the bar graphs we are going to ignore internal energy and draw the graph like this: BOTTOM Ug Ue K I Etot Etot = ½ kx2

6. Practice: ON A SEPARATE SHEET OF PAPER draw bar graphs for the following scenarios AND write the Etot equation. IGNORE INTERNAL ENERGY LOST TO HEAT. 1. A small car is pushed against a spring. It is then released and moves around a vertical loop. • Before it is released. Ug Ue K Etot Etot = ½ kx2

7. Practice: • When it is halfway up the loop. Ug Ue K Etot Etot = mgh + ½ mv2

8. Practice: • At the top of the loop. Ug Ue K Etot Etot = mgh + ½ mv2

9. Practice: d. At the bottom of the loop. Ug Ue K Etot Etot = ½ mv2

10. Practice: 2. A car rolls to a stop while moving up a hill. a. At the bottom of the hill. Ug Ue K Etot Etot = ½ mv2

11. Practice: b. Halfway up the hill. Ug Ue K Etot Etot = mgh + ½ mv2

12. Practice: c. After it stops rolling. Ug Ue K Etot Etot = mgh

13. Practice: 3. An arrow rests in a loaded bow, then it is launched straight UP into the air. a. Before the arrow is released. Ug Ue K Etot Etot = ½ kx2

14. Practice: b. Right as the arrow leaves the bow. Ug Ue K Etot Etot = ½ mv2

15. Practice: c. Halfway up. Ug Ue K Etot Etot = mghhalfway + ½ mv2

16. Practice: d. At the highest point. Ug Ue K Etot Etot = mgh

17. Practice: e. When the arrow reaches the ground. Ug Ue K Etot Etot = ½ mv2

18. Practice: 4. A bowling ball rolls down a hill and is stopped by a giant stretchy sling. a. At the top of the hill. Ug Ue K Etot Etot = mgh

19. Practice: b. Halfway down the hill. Ug Ue K Etot Etot = mghhalfway + ½ mv2

20. Practice: c. At the bottom of the hill BEFORE it reaches the sling. Ug Ue K Etot Etot = ½ mv2

21. Practice: d. After the sling has stopped it. Ug Ue K Etot Etot = ½ kx2

22. Practice: • Bob is jumping on his trampoline. a. He just jumped down and the trampoline is fully stretched. Ug Ue K Etot Etot = ½ kx2

23. Practice: b. He just barely left the surface of the trampoline. Ug Ue K Etot Etot = ½ mv2

24. Practice: • He is halfway up. Ug Ue K Etot Etot = mghhalfway + ½ mv2

25. Practice: d. He is all the way up. Ug Ue K Etot Etot = mgh

26. Practice: e. He is just barely reaching the trampoline again. Ug Ue K Etot Etot = ½ mv2

27. Practice: f. The trampoline is fully stretched again. Ug Ue K Etot Etot = ½ kx2

28. Pie Charts: Gravity Kinetic Elastic Heat or Internal Energy

29. Practice: Draw a PIE CHART for each of the following scenarios. This time you MUST acknowledge energy that is lost to heat. 1. A ball is held above the ground and then dropped so it falls straight down. a. At the very top: b. Halfway down: c. Right before it hits: mghtop mghmid + ½ mv2 + heat ½ mv2 + heat

30. Practice: 2. A wind-up toy is wound up, then it “walks” across the table and comes to a stop. a. Before it is released (but after it was wound up): b. Halfway across the table. c. After it has stopped. ½ kx2 ½ kx2 + ½ mv2 + heat heat

31. Practice: 3. A baseball is thrown up in the air and then falls back down. a. When it is first released. b. Almost at the top. c. At the very top. d. Halfway down. e. Right before it hits the ground. ½ mv2 mgh + heat mgh + ½ mv2 + heat ½ mv2 + heat mgh + ½ mv2 + heat

32. Practice: 4. A ball rolls to a stop on the floor. a. At the beginning. b. Halfway. c. After it stops. ½ kx2 ½ mv2 + heat heat

33. Practice: 5. A superball is dropped and bounces up and down. Draw a pie chart for each shown position of the ball. mgh mgh + heat ½ kx2 + heat mgh + heat ½ kx2 + heat

34. Practice: 6. An object rests on a coiled spring and is then launched upwards. a, Before launch. b. Right after it leaves the spring. c. When it is part way up. d. At the very top. ½ kx2 mgh + ½ mv2 + heat mgh + heat ½ mv2 + heat

35. Practice 7. A piece of clay is dropped to the floor. a. When it is first released. b. Halfway down. c. After it has struck the floor. mghtop mghmid + ½ mv2 + heat heat

36. Total Energy Total Energy = Potential + Kinetic Energy Ug Ug Ug+ K Ug+ K K

37. Total Energy • A skier is located at the top of a mountain. He is found to have an initial potential energy of 50,000 J. Fill in the blanks for the KE and PE as he skis down the mountain. 20, 000 J 30, 000 J 15, 000 J 0 J

38. Energy vs. Position Graphs • Use the first graph below to show the total, potential, and kinetic energy of the pendulum. E Potential Energy Kinetic Energy Total Energy x

39. If the total energy from the first graph was 10 J, how much would the potential and kinetic energy be where they cross? _______ If the potential energy is 8 J how much would the kinetic energy be? _______ 5 J 2 J E Potential Energy Kinetic Energy Total Energy x

40. Energy vs. Position Graphs • Make a similar graph showing the total, potential, and kinetic energy of the skier from the example above. Potential Energy Kinetic Energy Total Energy E x