1. Machines - Ch. 12 Introduction to Machines Work, Power, Energy
Mechanical Advantage
Simple Machines
Compound Machines

2. W = Fd Work Work transfer of energy through motion
force exerted through a distance
W = Fd
W: work (J)
F: force (N)
d: distance (m)
1 J = 1 N·m
Distance must be in direction of force!

3. B. Work
Brett’s backpack weighs 30 N. How much work is done on the backpack when he lifts it 1.5 m from the floor to his back?
GIVEN:
F = 30 N
d = 1.5 m
W = ?
WORK:
W = F·d
W = (30 N)(1.5 m)
W = 45 J F W d

4. B. Work d W F GIVEN: m = 40 kg d = 1.4 m - during d = 2.2 m - after
A dancer lifts a 40 kg ballerina 1.4 m in the air and walks forward 2.2 m. How much work is done on the ballerina during and after the lift?
GIVEN:
m = 40 kg
d = 1.4 m - during
d = 2.2 m - after
W = ?
WORK:
W = F·d F = m·a
F =(40kg)(9.8m/s2)=392 N
W = (392 N)(1.4 m)
W = 549 J during lift
No work after lift. “d” is not in the direction of the force. F W d

5. Power
Power
Rate at which work is done; how much work done in a given time
W = P t
W: work (J)
P: Power (Watt)
t: time (s)
1 J = 1 N·m
Distance must be in direction of force!

6. Power
It takes 100 kJ of work to life an elevator 18 m. If this is done in 20 s, what is the average power of the elevator during the process?
GIVEN:
W = 100 kJ
P = ?
t =20 s
WORK:
P = W÷t
P = ( J)÷(20)
P = 5000 W P W t

7. Energy ENERGY THERMAL The ability to cause change. MECHANICAL NUCLEAR
internal motion of particles
ENERGY
MECHANICAL
NUCLEAR
motion of objects
changes in the nucleus
ELECTRICAL
joules (J)
CHEMICAL
motion of electric charges
bonding of atoms

8. A. Energy Kinetic Energy (KE) energy in the form of motion
depends on mass and velocity
80 km/h
50 km/h
Which has the most KE?
Which has the least KE?
80 km/h truck
50 km/h motorcycle

9. Kinetic Energy
KE = ½ mv2
Kinetic energy depends on speed more than mass

10. Kinetic Energy
What is the kinetic energy of a 44 kg cheetah running at 31 m/s
GIVEN:
KE = ?
m = 44 kg
v =31 m/s
WORK:
KE = ½ (m) (v)2
KE = ½ (44) (31)2
KE = 2.1 x 104 J
KE = ½ mv2

11. A. Energy Potential Energy (PE) stored energy
depends on position or configuration of an object
Which boulder has greater gravitational PE?
What other ways can an object store energy?

12. PE = mgh Potential Energy m=mass, g=free-fall acceleration, h=height
g on earth=9.8 m/s2

13. Potential Energy PE = mgh
A 65 kg rock climber ascends a cliff. What is the climber’s gravitational potential energy at a point 35 m above the base of the cliff
GIVEN:
PE = ?
m = 65 kg
g =9.8 m/s2
h= 35 m
WORK:
PE = mgh
PE = (65)(9.8)(35)
PE = 2.2 x 104 J
PE = mgh

14. C. Conservation of Energy
Law of Conservation of Energy
Energy may change forms, but it cannot be created or destroyed under ordinary conditions.
EX:
PE  KE
mechanical  thermal
chemical  thermal

15. C. Conservation of Energy
PE  KE
View pendulum animation.
View roller coaster animation.

16. C. Conservation of Energy
Mechanical  Thermal
View rolling ball animations.
View skier animation.

17. A. Machines Machine device that makes work easier
changes the size and/or direction of the exerted force

18. B. Force Effort Force (Fe) force applied to the machine “what you do”
Also called Input Force
Resistance Force (Fr)
force applied by the machine
“what the machine does”
Also called Output Force

19. C. Work Win = Fe × de Wout = Fr × dr Work Input (Win)
work done on a machine
Win = Fe × de
Work Output (Wout)
work done by a machine
Wout = Fr × dr

20. C. Work Fe × de = Fr × dr Win = Wout Conservation of Energy
can never get more work out than you put in
trade-off between force and distance
Win = Wout
Fe × de = Fr × dr

21. C. Work Win = Wout Win > Wout In an ideal machine...
But in the real world…
some energy is lost as friction
Win > Wout

22. D. Mechanical Advantage
Mechanical Advantage (MA)
number of times a machine increases the effort force
Fr=resistance force
How much force the object has
Fe=Effort Force
How much force you use
MA > 1 : force is increased
MA < 1 : distance is increased
MA = 1 : only direction is changed

23. D. Mechanical Advantage
A worker applies an effort force of 20 N to open a window with a resistance force of 500 N. What is the crowbar’s MA?
GIVEN:
Fe = 20 N
Fr = 500 N
MA = ?
WORK:
MA = Fr ÷ Fe
MA = (500 N) ÷ (20 N)
MA = 25 MA Fr Fe

24. D. Mechanical Advantage
Find the effort force needed to lift a N rock using a jack with a mechanical advantage of 10.
GIVEN:
Fe = ?
Fr = 2000 N
MA = 10
WORK:
Fe = Fr ÷ MA
Fe = (2000 N) ÷ (10)
Fe = 200 N MA Fr Fe

25. D. Mechanical Advantage
If you do NOT have forces give, you can solve using distance
De=distance of effort (in meters)
What you do
Dr=Distance of resistance (in meters)
What machine does
MA > 1 : force is increased
MA < 1 : distance is increased
MA = 1 : only direction is changed

26. D. Mechanical Advantage
Using a block and tackle pulley, a boy pulls the rope 10 meters to move the weight up 2 meters. Find the MA
GIVEN:
MA = ?
De = 10 m
Dr = 2 m
WORK:
MA = De ÷ Dr
MA= (10 m) ÷ (2 m)
MA= 5 MA DE Dr

27. E. Efficiency (Honors) How well a machine works
No machine is 100% efficient
Many lose efficiency to friction, or energy lost as heat
Ex. If a machine is 90% efficient, it means 10% of the energy is lost as another form

28. E. Efficiency (Honors) Efficiency Formula:
Efficiency (%) Eff= Wout x 100
Win
Efficiency equal the work out divided by the work in multiplied by 100
Output is always less than the input work

29. Machines - Ch. 12 II. The Simple Machines Lever Pulley Wheel & Axle
Inclined Plane
Screw
Wedge

30. 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

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

32. 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

33. 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

34. A. Lever First Class Lever Fulcrum in the middle
can increase force, distance, or neither
changes direction of force
Examples: seesaws, scissors, pliers

35. A. Lever Second Class Lever Output force in middle
always increases force
Example: wheelbarrows, nutcrackers

36. A. Lever Third Class Levers Input force in middle
always increases distance
Examples: arms, legs, baseball bats

37. Three Classes of Levers

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

39. B. Pulley Ideal Mechanical Advantage (IMA)
equal to the number of supporting ropes on the load
You only count the end strand when it is pointed up!
IMA = 0
IMA = 1
IMA = 2

40. What is the IMA? =2 =3 =5

41. B. Pulley Fixed Pulley IMA = 1 (so no mechanical advantage!)
does not increase force
changes direction of force

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

45. B. Pulley Systems Block & Tackle
combination of fixed & movable pulleys
increases force (IMA = >1)
may or may not change direction

46. Pulley Systems

47. Pulley Systems

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

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

50. 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

51. 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

52. D. Inclined Plane Inclined Plane sloping surface used to raise objectsh l

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

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

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

56. 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

57. Compound Machines A machine made up of more than one simple machine
Ex: car, pair of scissors, bicycles