1. Chapter 5: Machines II. The Simple Machines Inclined Plane Lever Screw
Wedge
Lever
Pulley
Wheel & Axle

2. A. Lever
Lever
a bar that is free to pivot about a fixed point, or 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

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

4. A. Lever First Class Lever can increase force, distance, or neither
changes direction of force

5. A. Lever
Second Class Lever
always increases force

6. A. Lever
Third Class Levers
always increases distance

7. B. Pulley
Pulley
grooved wheel with a rope or chain running along the groove
a “flexible first-class lever” F Le Lr

8. B. Pulley Ideal Mechanical Advantage (IMA)
equal to the number of supporting ropes
IMA = 0
IMA = 1
IMA = 2

9. B. Pulley Fixed Pulley IMA = 1 does not increase force
changes direction of force

10. B. Pulley Movable Pulley IMA = 2 increases force
doesn’t change direction

11. B. Pulley Block & Tackle combination of fixed & movable pulleys
increases force (IMA = 4)
may or may not change direction

12. C. Wheel and Axle Wheel and Axle
two wheels of different sizes that rotate together
a pair of “rotating levers”
Wheel
Axle

13. C. Wheel and Axle Ideal Mechanical Advantage (IMA) effort radius
effort force is usually applied to wheel
axle moves less distance but with greater force
effort radius
resistance radius

14. Problems Lr Le Lr = 20 cm IMA = Le ÷ Lr Le = 140 cm
You use a 160 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

15. 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

16. 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

17. 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

18. D. Inclined Plane Inclined Plane h l
sloping surface used to raise objects h l

19. E. Screw
Screw
inclined plane wrapped in a spiral around a cylinder

20. F. Wedge
Wedge
a moving inclined plane with 1 or 2 sloping sides

21. F. Wedge Zipper 2 lower wedges push teeth together
1 upper wedge pushes teeth apart

22. Problems h Fe l MA Fr Fe = ? IMA = l ÷ h IMA = (3 m)÷(1.2 m)
How much force must be exerted to push a 450 N box up a ramp that is 3 m long and 1.2 m high?
IMA l h MA Fr Fe
GIVEN:
Fe = ?
Fr = 450 N
l = 3 m
h = 1.2 m
WORK:
IMA = l ÷ h
IMA = (3 m)÷(1.2 m)
IMA = 2.5
Fe = Fr ÷ MA
Fe = (450 N)÷(2.5)
Fe = 180 N