1. Work, Power, and Simple Machines

2. Work Work = Force x Distance The force must be in the direction
No Work
Work = Force x Distance
The force must be in the direction
of the motion, or no work is done.
Work

3. The unit of work is the Joule
Force x Distance = Work
1 Newton x 1 meter = 1 Newton meter
1 Newton meter = 1 Joule
James Prescott Joule

4. Example 1:
A high jumper weighs 700 newtons. What work does the jumper perform in jumping over a bar 2.0 meters high?
Answer: W = F x d
W = 700N x 2.0 m
= 1400 nm
= 1400 Joules

5. No work is done if there is no distance!
The statue of liberty has been holding up her torch for an awfully long time. How much work has she done?
Answer: 0! Although it takes a force to hold the torch against the force of gravity, there is no motion so no work is done.

6. Which does more work? Frictionless
The net work is the force (weight) of the cart x
the vertical distance. This is the same in all three
cases. In the first, the force is less, but distance is
greater to reach the same vertical height.

7. Example 2
A force of 200N is required to push a lawn mower. If 4000 J of work is performed on the lawnmower, how far does it move?
Answer: W__
F d
4000J__
200N d
4000Nm ÷ 200N
= 20m

8. Power = Force x distance
Work done per unit of time
Power = Work
Time
Power = Force x distance

9. The unit of power is the watt
Power = Work
Time
1 watt = Joule
Second

10. Example 3
A crane lifts a car into a junk pile in 10 seconds. What is the crane’s power if 120,000 J of work are performed?
Answer: Power = Work
Time
120,000J =
10 sec
12,000 Watts

11. Power = Force x distance
Example 4
A 750 N diver does a somersault off a 10m platform. It takes her 1.5 seconds to hit the water. What is her power?
Since work is Force x distance, the power formula can be written as
Power = Force x distance
Time

12. Answer: Power = 750N x 10m Power = 7500N m Time 1.5 sec = 5000 Watts
Power = Force x distance
Time
Power = 750N x 10m
1.5 sec
Power = N m
= Watts

13. Other units of power 1 kilowatt = 1000 watts 1 horsepower = 750 watts
In the previous example, how many kilowatts power was generated? How much horsepower?

14. Answer: 5000 watts ÷ 1000 kw/w = 5 kilowatts
5000 watts ÷ 750 hp/w = 6.7 horsepower

15. Work, mechanical advantage, and efficiency
Machines
Work, mechanical advantage, and efficiency

16. Machines make work easier
Machines change the size or direction of the applied force.

17. 2 forces are involved in machines
FE = effort force
The force applied to the object
FR = resistance force
The force that opposes effort. Often equal to the weight of the object. FE FR

18. Machines move a force through a distance
Effort distance
The distance through which the force is applied
Resistance distance
The distance the object
moves DE DR

19. Work in = work out (neglecting friction)
WI = work input
The work done on a machine
Wo = Work output
The work done by the machine

20. DE = 5ft DR = 5ft For a lever, the effort distance
and resistance distance can
be measured from the fulcrum.
In this case, we call them the effort arm and resistance arm.
DE = 5ft
DR = 5ft

21. What is the work input and work output? DE = 5ft DR = 5ft
10 lbs x 5 feet =
50 ft lbs
DR = 5ft

22. Find FE, the force required to balance the seesaw:
DE = 2ft
DR = 8ft

23. Answer: FE =40 lbs Work output = work input FR • dR = FE • dE
10 lbs • 8ft = x lbs • 2ft
80 = 2x
x = 40 lbs
FE =40 lbs FR
DE = 2ft
DR = 8ft

24. Find the effort force: 6.7 lbs Work output = work input DE = 6ft
4(10) = 6x
40 = 6x
x = 6.7 lbs
DE = 6ft
DR = 4ft

25. Mechanical = Resistance force_ MA = FR_
Mechanical Advantage
Number of times a machine multiplies effort
Mechanical = Resistance force_
Advantage Effort force
MA = FR_ FE

26. 1 What is the mechanical advantage? DE = 5ft DR = 5ft
10 lbs ÷ 10 lbs = 1
DR = 5ft

27. What is the mechanical advantage?
MA = FR_ FE
40 lbs
= 10lbs ÷ 40 lbs
= 0.25
DE = 2ft
DR = 8ft

28. Find the mechanical advantage:
6.7 lbs
MA = FR_ FE
= 10 lbs ÷ 6.7 lbs
= 1.5
DE = 6ft
DR = 4ft

29. What does mechanical advantage mean?
A mechanical advantage of one has no effect on the force required
A mechanical advantage of less than one makes it harder for you to do the work
A mechanical advantage greater than one makes the work easier.

30. Efficiency Compares work output to work input
Can never be greater than 100%
Machines can never give out more work than is put in
Friction reduces efficiency

31. Efficiency FE = 50N Work output Work input Expressed as a percent
Example: A box is slid up an incline with a force of 50N. The length of the incline is 7 meters, and its height is 5 meters. The box weighs 70N. What is the efficiency?
FR = 70N
dR = 5m
FE = 50N
dE = 7m

32. Answer: FE = 50N Work output = FR x dR Work input FE x dE = 70N x 5m
= 350
350
= 1
= 100%
FE = 50N
FR = 70N
dR = 5m
dE = 7m

33. Describe the friction from the last example
FRICTIONLESS!!
100% efficient

34. Efficiency with friction
Example: A box is slid up an incline with a force of 100N. The length of the incline is 7 meters, and its height is 5 meters. The box weighs 70N. What is the efficiency?
FR = 70N
dR = 5m
FE = 100N
dE = 7m

35. Answer: FE = 100N Work output = FR x dR Work input FE x dE = 70N x 5m
= 350
700
= 0.5
= 50%
FE = 100N
FR = 70N
dR = 5m
dE = 7m

36. Simple machines

38. Levers
The resistance and effort move about the fulcrum.

39. Levers: 3 types
First class
Third class
Second class

40. E First class lever R F Resistance Effort Fulcrum:
Fulcrum is between effort and resistance F
Resistance
Effort
Fulcrum

41. R F E resistance effort Fulcrum 2nd Class Levers
The resistance is located between
the effort force and the fulcrum. E
resistance
effort
Fulcrum

42. R E F
Second class lever

43. The effort force is located between
3rd Class Levers
The effort force is located between
the resistance force and the fulcrum. E F
Effort
Resistance
Fulcrum

44. R F
Third class lever E

45. What class lever?
Second class
Resistance in the middle

46. What class lever?
First class
Fulcrum in the middle

47. What class lever?
First class
Fulcrum in the middle

48. What class lever?
Second class
Resistance in the middle

49. What class lever?
Third class
Effort in the middle

50. What class lever?
Third class
Effort in the middle

51. What class lever?
Effort in the middle
Third class

52. What class lever?
Second class
Resistance in the middle

53. How are the force and distance related in a machine?
Less force requires a greater
distance to do the same amount of work.

54. If the 20kg frog sits 8 meters from the fulcrum, where should the 5kg
frog sit to balance?
20(8) = 5(x)
32 m = x
32 m from the fulcrum

55. WHEEL AND AXLE: a lever rotating in a circle

56. Wheel and axle examples

57. Inclined Plane: any sloping surface used to raise objects, such as a ramp

58. Inclined plane

59. Inclined plane

60. The ideal mechanical advantage of an inclined plane is length ÷ height.
What is the ideal mechanical advantage?
10m ÷ 2m = 5
Length = 10m
Height
= 2m

61. The actual mechanical advantage of an inclined plane is resistance ÷ effort.
What is the actual mechanical advantage?
24N ÷ 6N = 4
Why is AMA<IMA?
Effort = 6N 
FRICTION!
Resistance (the weight
of the cart) = 24N

62. What is the efficiency of this inclined plane?
Work output ÷ work input
FR x dR = 24N x 2m
FE x dE N x 10m
= 48 = .8 60
80%
Effort force = 6 N 
Resistance force (the weight
of the cart) = 24N
Height = 2m
Length = 10m

63. SCREW: an inclined plane wrapped around a cylinder to form a spiral
A screw multiplies effort by acting through a long effort distance.

64. WEDGE: an inclined plane that moves.

65. PULLEY: a rope, belt, or chain wrapped around a wheel

66. Fixed pulley No mechanical advantage
Changes the direction of the force.

67. Moveable pulley Pulley is not connected to anything.
This pulley has an ideal mechanical advantage of 2.

68. Combined pulleys A single fixed and a single moveable.
This pulley system has an ideal mechanical advantage of 2.

69. The ideal mechanical advantage of a pulley system is found by counting the number of ropes that pull up.
MA = 2
MA = 3
MA = 4

70. What is the ideal mechanical advantage of this system?3

71. Effort equals resistance!
The ideal mechanical advantage of a pulley system is found by counting the number of ropes that pull up.
What is the ideal mechanical advantage of this pulley? 1
Effort equals resistance!

72. To Review:
6 simple machines are:
lever
wheel and axle
inclined plane
wedge
screw
pulley

73. To review: Work = force x distance power = work ÷ time
mechanical advantage = resistance force ÷ effort force
efficiency = work output ÷ work input

74. That's All Folks!!