1. Machines The Simple Machines Lever Pulley Wheel & Axle Inclined Plane
Screw
Wedge

2. Objectives Identify the types of levers and pulleys.
Calculate ideal mechanical advantage.
CLE Demonstrate the relationship among work, power, and machines.

3. A. Simple Machines
A machine that does work with only one movement is a simple machine .
There are six simple machines: lever, pulley, wheel and axle, inclined plane, screw and wedge.

4. B. Lever
Lever
a bar that is free to pivot about a fixed point called a fulcrum
“Give me a place to stand and I will move the Earth.”
– Archimedes
Engraving from Mechanics Magazine, London, 1824
Resistance
arm
Effort arm
Fulcrum

5. B. Lever – 3 Parts 1. Fulcrum – the fixed point on a lever.
2. Effort arm – part of the lever on which effort force is applied.
3. Resistance arm – part of the lever that exerts the resistance force.

6. B. Lever
4. There are three classes of levers based on positions of effort arm, resistance arm, and fulcrum.

7. Lever
First-class lever – fulcrum is located between the effort and resistance forces; always multiplies and changes direction of force.

9. Lever
First Class Levers

10. Lever b. Second Class Lever -
resistance force is located between the effort force and fulcrum; always multiplies force.

12. Lever
Second Class Lever

13. A. Lever C. Third Class Levers
effort force is between the resistance force and fulcrum; doesn’t multiply force but does increase distance over which force is applied.

15. Third Class Levers
                        
(Hammer hitting nail)

17. Which Class?
Second Class Lever

20. Levers

21. Review -
Mechanical advantage (MA) is the number of times a machine multiplies the effort force.
Calculated:
MA = resistance force/effort force

22. Lever
5. Calculating ideal mechanical advantage (IMA) of a lever – IMA equals length of effort arm divided by length of resistance arm. IMA = L(e) / L(r)
6. MA can be increased by making the resistance arm longer.

23. Lever Le must be greater than Lr in order to multiply the force.
7. Ideal Mechanical Advantage (IMA)
frictionless machine
Effort arm length
Resistance
arm length
Le must be greater than Lr in order to multiply the force.

24. C. Pulley
A grooved wheel with a rope, simple chain or cable running along the groove.
The axle of the pulley acts as the fulcrum.

25. 1. Fixed Pulley a. A fixed pulley is attached to something that
doesn’t move such
as ceiling or floor
(flagpole)
b. Force is not
multiplied but
direction is changed
so IMA = 1

26. Fixed Pulley
c. A fixed pulley is a modified first-class lever.
                         

27. 2. Movable Pulley
A movable pulley has one end of the rope fixed and the wheel free to move; (construction crane) multiplies force; IMA = 2

28. Movable Pulley
                         

29. 3. Block and Tackle Pulley
System of pulleys consisting of fixed and movable pulleys; IMA = number of ropes supporting resistance weight (count the wheels).

30. 4. Pulley - IMA Ideal Mechanical Advantage (IMA)
equal to the number of supporting ropes or wheels
IMA = 0
IMA = 1
IMA = 2

31. 4. Pulley - IMA

32. 4. Pulley - IMA

33. Simple Machines
D. Wheel and Axle
1. A wheel and axle is a simple machine consisting of a shaft or axle attached to the center of a larger wheel, so that the wheel and axle rotate together.

34. D. Wheel and Axle Two wheels of different sizes that rotating together
A pair of “rotating levers”
Modified lever
Wheel
Axle

35. D. Wheel and Axle
Doorknobs, screwdrivers, and faucet handles are examples of wheel and axles. Doorknob – the larger part is the wheel and smaller part is the axle; crank – lever attached to a shaft.
Effort force usually applied to the larger wheel

36. D. Wheel and Axle IMA = radius of wheel divided by the radius of axle.
Note: it is a modified lever form.

37. D. Wheel and Axle Ideal Mechanical Advantage (IMA)
effort force is usually applied to wheel
axle moves less distance but with greater force
The center of the axle is the fulcrum
effort radius
resistance radius

38. Wheel and Axle

39. Wheel and Axle
5. Gears are modified form of the wheel and axle.

40. Wheel and Axle
Several
examples
of the wheel
& axle are
pictured here

41. Problems Lr Le Lr = 20 cm IMA = Le ÷ Lr Le = 140 cm
You use a 140 cm plank to lift a large rock. If the rock is 20 cm from the fulcrum, what is the plank’s IMA?
GIVEN:
Lr = 20 cm
Le = 140 cm
IMA = ?
WORK:
IMA = Le ÷ Lr
IMA = (140 cm) ÷ (20 cm)
IMA = 7
IMA Le Lr
20cm
160cm

42. Problems rr re re = 20 cm IMA = re ÷ rr rr = 5 cm
A crank on a pasta maker has a radius of 20 cm. The turning shaft has a radius of 5 cm. What is the IMA of this wheel and axle?
GIVEN:
re = 20 cm
rr = 5 cm
IMA = ?
WORK:
IMA = re ÷ rr
IMA = (20 cm) ÷ (5 cm)
IMA = 4
IMA re rr
20 cm
5 cm

43. Problems rr re IMA = 6 re = IMA · rr re = ? re = (6)(4 cm) rr = 4 cm
A steering wheel requires a mechanical advantage of 6. What radius does the wheel need to have if the steering column has a radius of 4 cm?
GIVEN:
IMA = 6
re = ?
rr = 4 cm
WORK:
re = IMA · rr
re = (6)(4 cm)
re = 24 cm
IMA re rr rr re

44. Problems Lr Le Fr = 150 N Le = IMA · Lr Fe = 15 N Le = (10)(0.3)
You need to lift a 150 N box using only 15 N of force. How long does the lever need to be if the resistance arm is 0.3m?
GIVEN:
Fr = 150 N
Fe = 15 N
Lr = 0.3 m
Le = ?
MA = 10
WORK:
Le = IMA · Lr
Le = (10)(0.3)
Le = 3 m
Total length = Le + Lr
Total length = 3.3 m
15N
0.3m ?
150N
IMA Le Lr

46. Objectives Identify the types of levers and pulleys.
Calculate ideal mechanical advantage.
CLE Demonstrate the relationship among work, power, and machines.