1. Work, Energy, Power

2. Work
Defined as “the transfer of energy by mechanical means.”

3. “Work is done when a constant force is exerted on an object in the direction of motion, times the object’s displacement."
Examples – work or not?
A mom walking a stroller across the street
A teacher pushing against the wall for five minutes
A book falls off a table and free falls to the ground
A rocket accelerates through space
A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed
There are three key ingredients to work - force, displacement, and cause. In order for a force to qualify as having done work on an object, there must be a displacement and the force must cause the displacement.

4. Work Notes Units are in… Large or Small?
Joules ( J ) which are Newton-meters
Large or Small?
1 calorie = heat required to 1 gram of H2O up 1 degree Celsius
Average candy bar has 250 calories – but food calories are Kcal
so 250,000 calories! Only enough to raise the temperature of the water in a 250 lb. man 3 degrees C.
1 calorie = joules

5. Work Notes
Mathematically speaking…
W = Fd

6. Work Practice
W = ? F = 200 N d = 5 m W = F • d W = 200 N • 5 m W = 1000 J
W = ?
F = 50 N
d = 0.15 m
W = F • d
W = 50 N • 0.15 m
W = 7.5 J

7. Work Practice
F = ? W = 50 J d = 0.5 m W = F • d F = W/d F = 50 J / 0.5 m F = 100 N
d = ?
W = 1.5E4 J
F = 5000 N
W = F • d
d = W/F
d = 1.5E4 J / 5000 N
d = 3.0 m

8. Work Notes
What if the force is not exactly in the same direction…
W = F d cosθ
There are three key ingredients to work - force, displacement, and cause. In order for a force to qualify as having done work on an object, there must be a displacement and the force must cause the displacement.

9. Work Practice
W = ? F = 200 N d = 5.00 m Θ= 30.0° W = F •d • cosΘ W = 200 N • 5 m • cos 30° W = 866 J
W = ?
F = 50 N
d = 0.15 m
Θ= 45°
W = F •d • cosΘ
W = 50 N • 0.15 m • cos 45°
W = 5.3 J

10. Power
Defined as “the rate that work is done.”

11. “Power is equal to the work done, divided by the time taken to do the work."
In work, time is not a factor, but in Power it is…
Units are in…
Watts ( W )
that is, 1 J (Joule) of energy transferred in 1 s (second)

12. Power Notes
Mathematically speaking…

13. Power Practice
P = ? F = 200 N d = 5 m t = 5 s P = W / t P = F • d / t P = 200 N • 5 m / 5 s P = 200 W
P = ?
F = 1000 N
d = 50 m
t = 2 s
P = W / t
P = F • d / t
P = 1000 N • 50 m / 2 s
P = W

14. Energy
Defined as “the ability of an object to produce a change in itself or in the world around it.”

15. “Energy is the ability to do work."
Examples – ways ENERGY is stored…
Heat or thermal energy
Nuclear energy
Chemical energy
Electrical energy
In physics –we are concerned with…
Kinetic Energy - KE
Potential Energy – PE
Mechanical Energy – ME or TME– the sum of KE and PE when no other forms of energy are present

16. Kinetic Energy Notes Units are same as work units…
Joules ( J )
Kinetic Energy - energy resulting from motion
“The kinetic energy of an object is equal to ½ times the mass of the object multiplied by the speed of the object squared.”

17. Kinetic Energy Notes
Mathematically speaking…
KE = ½mv²

18. Kinetic Energy Practice
KE = ? m = 60.0 kg v = 9.00 m/s KE = ½mv² KE = ½ • 60.0 kg • (9.00 m/s)² KE = 2.43E3 J

19. Energy Practice
KE = ? m = 2.30E4 kg v = 260 m/s KE = ½mv² KE = ½ • 2.30E4 kg • (260 m/s)² KE = 7.77E8 J

20. Work, Energy, Power, Momentum, and Machines Hour 2

21. Potential Energy Notes
Units are same as work units…
Joules ( J )
Potential Energy – stored energy resulting from gravity pulling the object towards Earth.
(There are other forms to consider later…)
“The potential energy of an object is equal to the mass of the object multiplied by the acceleration due to gravity times the height above the ground state.”

22. Potential Energy Notes
Mathematically speaking…
PE = mgh

23. Potential Energy Practice
PE = ? m = 7.25 kg h = 2.00 m PE = m g h PE = 7.25 Kg • 9.8 m/s² • 2.00 m PE = 142 J

24. Potential Energy Practice
PE = ? m = 2.30E4 Kg h = m PE = m g h PE = 2.30E4 Kg • 9.8 m/s² • m PE = 2.93E9 J

25. Mechanical Energy Notes
Mechanical Energy – sum of KE and PE when no other forms of energy are present.
Mathematically speaking…
E = KE + PE
Units are still (J) Joules!!!

26. Mechanical Energy Practice
m = 2.30E4 Kg
h = 6500 m
v = 260 m/s
E = KE + PE
E = ½mv² + mgh
E = ½ • 2.30E4 kg • (260 m/s)² E4 Kg • 9.8 m/s² • 6500 m
E = 2.24E9 J

27. Conservation of Energy
“It’s the Law!”

28. W = ΔKE Work-Energy Theorem
“Work is equal to the change in kinetic energy.”
W = ΔKE
Important because “if there is no change in kinetic energy then no work is done.”
You must do work on a system to put energy into it.

29. Conservation of Energy Notes
The Law of Conservation of Energy states that…
… “in a closed , isolated system, energy can neither be created nor destroyed; rather, energy is conserved.”
The total energy of the system remains constant – however, energy can change forms.
Ei = Ef

30. Conservation of Energy Notes
PE = 142 J
KE = 0 J
PE = 71 J
KE = 71 J
PE = 0 J h
KE = 142 J
½ h

31. C of E Notes
Mathematically speaking…
Ei = Ef
KEi + PEi = KEf + PEf

32. ½mv²i + mghi = ½mv²f + mghf
C of E Notes
Mathematically speaking…
KEi + PEi = KEf + PEf
PE = mgh & KE = ½mv²
½mv²i + mghi = ½mv²f + mghf

33. C of E Practice
v = 3.00 m/s
m = 7.25 kg h = 2.00 m v = 3.00 m/s ½mv²i + mghi = ½mv²f + mghf ½(7.25)(0)² (9.8)(2) = ½(7.25)(3)² (9.8)hf (9.8)(2) = ½(7.25)(3)² (9.8)hf hf = ( ) / 71.1 hf = 1.54 m hf
DRAWING NOT TO SCALE

34. C of E Practice
60.0 m
100.0 m hf
m = 50.0 kg hi = m v = ? ½mv²i + mghi = ½mv²f + mghf vf = vf = vf = 34.3 m/s
DRAWING NOT TO SCALE

35. Why not just use kinematics for Energy problems?

36. C of E Practice
A pendulum of length 1.0 meter is pulled back along its path and held a height of meters above its lowest position and is then released. How fast will the bob be moving when it swings to the lowest point? Ei = Ef ½mv²i + mghi = ½mv²f + mghf vf = vf = vf = 2.6 m/s
1.0 m
0.35 m
DRAWING NOT TO SCALE

37. C of E Practice A
m = 50.0 kg hA = 20.0 m hB = 10.0 m hC = 0.00 m vA = 10.0 m/s Ei = Ef PE KE ME v hD = 4.69 m
v = m/s hA B hB D C
DRAWING NOT TO SCALE A B C D
9800 J
4900 J
0 J
2300 J
2500 J
7400 J
12,300 J
10,000 J
10.0 m/s
17.2 m/s
22.2 m/s
20.0 m/s