1. Work and Energy Work Kinetic Energy Work – Energy Theorem
Gravitational Potential Energy
Mechanical Energy
Conservation of Energy

2. Starter The angle between two vectors is found by placing their tails
together and picking the smallest angle between them. For example,
the angle between B and D is 45 degrees. Find the angle between:
A and B
B and C
3. C and D
4. A and E o o o o

3. Practice - Work

4. Work = Frcos(q) Units = Joules
F = magnitude of the force
r = magnitude of the displacement
q = the angle between F and r

5. Example Work = Frcos(q) = 100(2)cos30 = 173J
A 100N force acts on a box at 30 degrees with respect to the horizon,
moving the box 2m to the right. How much work did the force do?
F = 100N r = 2m q = 30 degrees
Work = Frcos(q) = 100(2)cos30 = 173J

6. Example
Find the total work done on this box as it moves 3m to the right.
Work done by P: W = 200(3)cos(0) = 600J
Work done by N: W = Nrcos(90) = 0
Work done by f : W = 80(3) cos(180) = -240J
Work done by Weight : W = 100(3)cos(90) = 0
Total Work = (-240) + 0 = 360J

7. Kinetic Energy – Energy of Motion
KE = (1/2)mv2
Example: Find the kinetic energy of a 20kg mass moving at 10 m/s.
KE = (1/2)mv2 = (1/2)(20)(10)2 = 1000J
Example: If you double your velocity, what happens to the KE?
KE (new) = (1/2)m(2v)2 = 4KE(original)

8. Work Energy Theorem
Work Total = ½mvf2 – ½mvi2 or
Work Total = DKE

9. Example
If this box starts at rest, what is its velocity after it moves 3m?
Previously we saw that the total work was 360J.
Work Total = (1/2)mvf2 – (1/2)mvi2
360 = (1/2)(10)vf2
vf = 8.48 m/s

10. Example
If a mass is dropped from rest 20m above the ground, how fast is it moving when it hits the ground?
Work Total = (1/2)mvf2 – (1/2)mvi2 = (1/2)mvf2
Work = Frcosq = mgrcos(0) = mgr = (1/2)mvf2
vf = [ 2gr ] ½ = [ 2(9.8)(20) ] ½ = m/s

11. Starter 75J 105J 315J None of these.
A golf ball moving at 40 m/s has a kinetic
energy of 35 Joules. What is its kinetic energy
if it instead moves at 120 m/s?
75J
105J
315J
None of these.

12. Starter #2
At the top of her swing, 2 meters from the
ground, a child has a potential energy of
500 Joules. When she is 1m from the ground, her
kinetic energy is
500J
300J
250J
150J.

13. Energy of Motion – Kinetic Energy
Energy Types
Energy of Motion – Kinetic Energy
Stored Energy – Potential Energy

14. Gravitational Potential Energy
The work you do to lift an object is
equal to its increase in gravitational PE.
PE = mgh
h = vertical distance from ground level.

15. Example Work = increase in PE = mgh = 100(9.8)10 = 9800 Joules.
How much work does a 100kg person do walking up a flight of stairs
that takes her 10m off of the ground?
Work = increase in PE = mgh = 100(9.8)10 = 9800 Joules.
(Note: 1 Calorie = 4128J, so this person burned a little over 2 calories. )
( Note: 1 taco = 200 Calories = 825,600 Joules)

16. Total Mechanical Energy, E
E = KE + PE
If there is no friction, the total mechanical energy is conserved.
This means KE + PE is always the same number.
So if KE drops, PE must rise. If PE drops, KE must rise.
Another way to say this, is that KE is converted to PE, or PE is converted to KE.

17. Conservation of Energy

18. Example
A 1 kg rock is dropped from rest from a building 20m high. Fill in the table.
Height KE PE E 20 10 5
PE at the top is mgh =
1(9.8)(20) = 196J
196J
196J
KE at the top is zero.
98J
196J
98J
147J
49J
196J
E at the top (and everywhere)
is J = 196J
196J
196J
PE at the bottom is zero…………

19. Practice/ Application
Open the “ Energy Skate Park Basics” at the phet site.
In the “ Introduction” tab, pick the first track (U shaped.)
Check “ bar graph” , “speed”, “grid” and “slow motion”.
Place the skater at 4m above the ground on the track and release.

20. Data Put in Science Notebook
Read and record the velocity at the following heights.
Each increment on the speed dial is 1.0m/s
h(m)
v(m/s)
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

21. Questions - Put in Science Notebook
Describe how the kinetic energy and the potential energy are
related by observing the bar graph.
a. What can you tell about the sum of KE and PE?
b. When the KE is a maximum, what is the PE?
c. How is the KE related to the velocity?
d. How is the PE related to the height?
2. At what height are the potential energy and the kinetic energy equal?
How are h and v related? Are they directly proportional?
Plot v2 vs. h and do a best fit for the graph. What does this tell you about
the relationship between h and v?

22. Exit In your science notebook, answer the following:
1. What are the factors that determine
potential energy?
2. What are the factors that determine
kinetic energy?

23. Science Notebook Checklist
Starter
Data table
3 Answered Questions
Graph ( v2 vs. h )
Summary
Exit

24. Starter A 10kg rock is moving at 10m/s and is 10m
above the ground. What is its total energy, E?
KE = (1/2)mv2 = (.5)(10)(102) = 500J
PE = mgh = 10(9.8)10 = 980J
E = PE + KE = 1480J

25. Summary Work = Frcos(q) E = KE + PE KE = (1/2)mv2 PE = mgh
Work Total = ½mvf2 – ½mvi2 or
Work Total = DKE
PE = mgh
E = KE + PE

26. Introduction to Energy Skate Park Lab
Starter : At what points on the path of a
swinging child is her speed a maximum?
A minimum? How does this relate to the
height of the child above the ground?