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: MIDDLE Ug Ue K I Etot Etot = mghmid + ½ mv2
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: BOTTOM Ug Ue K I Etot Etot = ½ kx2
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.
Post answers around the room for bar graphs and pie charts and have them check their answers after they have taken them home and worked on them.
Ug Ue K Etot
Etot = ½ kx2

7. When it is halfway up the loop.
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. d. At the bottom of the loop.
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. c. After it stops rolling.
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. b. Right as the arrow leaves the bow.
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. e. When the arrow reaches the ground.
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. b. Halfway down the hill. Practice: Ug Ue K Etot
Etot = mghhalfway + ½ mv2

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

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

22. Bob is jumping on his trampoline.
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. b. He just barely left the surface of the trampoline.
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. e. He is just barely reaching the trampoline again.
Practice:
e. He is just barely reaching the trampoline again.
Ug Ue K Etot
Etot = ½ mv2

27. f. The trampoline is fully stretched again.
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
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 + ½ mv2 + heat
mgh + heat
mgh + ½ mv2 + heat
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
½ kx2 + heat
mgh + heat
½ kx2 + heat
mgh + 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
½ mv2 + heat
mgh + ½ mv2 + heat
mgh + 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

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