1. Work, Energy, Power Chapter 6 in a nutshell
Work is Force times Distance.
The change in Kinetic Energy is equal to the work.
Power is Work per unit time.

2. New Concept: Kinetic Energy
K = ½ m V2
Work causes a change in kinetic energy, so the units are the same.
Units of Kinetic energy: Joule
But, from the definition of kinetic energy, the units are also,
1 Joule = 1 Kg-m2/s2

3. Table 7-1 Typical Values of Work
Activity
Equivalent work (J)
Annual U.S. energy use
8 x 1019
Mt. St. Helens eruption
1018
Burning one gallon of gas
108
Human food intake/day
Melting an ice cube
107
104
Lighting a 100-W bulb for 1 minute
6000
Heartbeat
0.5
Turning page of a book
10–3
Hop of a flea
10–7
Breaking a bond in DNA
10–20

4. Work is force times distance…but!
Only the force component in the direction of motion counts!
Units of work: Joule

5. Force in direction of motion is what matters…
Fx = F cosq D
W = D * F cosq

6. Figure 7-3 Force at an Angle to Direction of Motion: Another Look

7. I’ve got work to do…. W=F*Dy=MgH F = Mg F = Mg Dy
This is the work done by the person lifting the box.

8. How about the reverse?…. W=F*Dy = - MgH F = Mg
Work can be positive or negative.
Lifting a box is positive work.
Lowering the box is negative work. H
F = Mg

9. Positive or Negative? Work done by gravity. Fg = - Mg
Work “done by force of gravity” is positive when an object is dropped.
Dy = - H

10. Problem 7-77
W = 50J, given v, F, x.
What is theta?
What is M?

11. Figure 7-4 Positive, Negative, and Zero Work

12. Raindrops are falling on my head….V1
F = - Mg
Dy = -H V2

13. Special case: Object dropped from rest.
Mass M dropped from height H. What is speed just before hitting the ground? (Neglect friction of air)
-Mg
W=MgH H
W=DK=1/2 M v2

14. Thought provoking: The inclined plane.
Distance = h
Force = mg
W = mgh
Distance = L = h/sin q
Force = mg sin q
W = mgh
The work is the same in both cases. This is an example of conservation of energy, which we will see much more of in the future.

15. How about the speed? F=Mg sinq H q
If Block fell straight down through height H, its speed would be:
Use F=Ma to find speed down the ramp.
But a = g sinq
And L = H/sinq
V=at
L=1/2 a t2 so
So…
Same magnitude of speed, but DIFFERENT DIRECTION!

16. Figure 7-6 Graphical Representation of the Work Done by a Constant Force

17. Figure 7-7 Work Done by a Non-Constant Force

18. Figure 7-8a Work Done by a Continuously Varying Force

19. Figure 7-8b Work Done by a Continuously Varying Force

20. Figure 7-8c Work Done by a Continuously Varying Force

21. When force is not constant.
The area under a force-distance curve is the work, W.
The average force times the distance gives the work. This is the same as the area under the curve.
Force
Distance

22. Back to our Spring Flings.
F = K Dx
How much work is done to move the block?
Be careful with the signs of the forces!
The force to move the block must be equal and opposite to the force of the spring on the block.
F = -K Dx
F=Kx
Force
W = ½ F X
W = ½ K X2
Work done to move a mass on a spring a distance “x”:
Distance X

23. Conceptual Checkpoints
What is work, in physics terms?
What is kinetic energy?
What is power?
Work is force in the direction of motion.
Kinetic energy is ½ Mv2
Power is Work (or Energy) per Unit time.

24. Work and the Weightlifter
A weightlifter performs three steps. What is the work done for each of the steps? Assume the weight is 100 Kg, the height of the lift is 1 M, and the acceleration of gravity is 10 M/s^2.
Work done against gravity to lift an object a height H is W = MgH
Cheryl Hawarth, USA gold medal.
W1: The weight is lifted up to the height of 1 M.
W2: The weight is held at 1M for 5 seconds.
W3: The weight is lowered down to the ground.

25. Weightlifting Work. 1000J, 5000J, 1000J 1000J, 0J, -1000J
W1: The weight is lifted up to the height of 1 M.
W2: The weight is held at 1M for 5 seconds.
W3: The weight is lowered down to the ground.
The work done W1, W2, W3 is:
1000J, 5000J, 1000J
1000J, 0J, -1000J
1000J, 5000J, -1000J
Cross-Tab Label
0 / 100

27. The energy is kinetic, relatively speaking….
V = + 5 m/s
V = -5 m/s
Train moves to the right with speed V. A baseball is thrown to the left with the same speed.
What is the kinetic energy of the baseball? Its mass is 1 kg.

28. What is the kinetic energy?
0 / 100
What is the kinetic energy?
V = + 5 m/s
V = -5 m/s
K = ½ M V2
M = 1 kg
12.5 J
5 J
Zero
Either zero or 12.5J, depends on your frame of reference.
Cross-Tab Label

29. The Power to overcome Friction.
Work is Force times distance. Power is Work per unit time.
AN IMPORTANT SPECIAL CASE
Block moves with STEADY SPEED under influence of applied force that EXACTLY balances friction, so V is CONSTANT.
Under these conditions,
Force of friction F
Frictional Force, Ff = mN
THIS IS A SPECIAL CASE IN WHICH AN APPLIED FORCE RESULTS IN CONSTANT SPEED.
IT OCCURS BECAUSE THE NET FORCE IS ZERO (SUM OF ALL APPLIED FORCES).

30. How about this case?
Total work is just the sum of the work for each spring.

31. And this one?
This is harder. The two springs DO NOT stretch the same distance (they have different K values).
But F1 = F2 (why?), so let it be called F.
So, can create an effective spring constant, Keff,
Then, we can apply the usual formula: