1. Chapter 6
Work and Machines

2. W = Fd A. Work W: work (J) F: force (N) d: distance (m) 1 J = 1 N·m
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. d W F GIVEN: m = 40 kg d = 1.4 m - during d = 2.2 m - after W = ?
B. Work
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. B. Power
Power
Amount of work done in a certain amount of time. (aka the “rate” work is done)
SI Units are in watts (W)
P = W/t

6. GIVEN: W = 900 J t = 5 s P = ? WORK: P = W/t P = 900 J/ 5s
B. Power
You do 900 J of work in pushing a sofa. If it took 5 seconds to move the sofa, what was your power?
GIVEN:
W = 900 J
t = 5 s
P = ?
WORK:
P = W/t
P = 900 J/ 5s
P = 180 J/s or watts (W)

7. P = Etransferred/t B. Power Power and Energy
Doing work is a way of transferring energy from one object to another
Work = Energy transferred
P = Etransferred/t

8. GIVEN: P = 120 J t = 1 hr E = ? WORK: P = E/t or E = Pt B. Power
A color TV uses 120 W of power. How much energy does the TV use in 1 hour?
GIVEN:
P = 120 J
t = 1 hr
E = ?
WORK:
P = E/t or E = Pt
t = 1 hr(60 min/1 hr)(60 sec/1 min)
t = 3600 s
E = 120 J/s (3600s)
E = 432,000 J

9. Bell Work
A 600 kg great white shark is lurking below an observation cage. His movement is being studied from a series of motion sensors below the boat. The shark leisurely charges the cage, strikes it and makes the cage rattle. Later, the shark returns for another run at the cage. The shark strikes the cage with 12,800 N of force. The shark traveled for 10 m in making its run. The cage is designed to withstand 124,500 N-m (J) of “work” before it breaks. Should the man in the cage be worried? Explain.

10. Section 2

11. A. Machines
Machine
device that makes work easier

12. There are four ways that a machine helps us to do work.
Transfers our effort force from one place to another. Ex: seesaw
Multiply your effort force Ex: crowbar
Magnify speed and distance Ex: baseball bat
Changing the direction of the force. Ex: pulley on the flagpole

13. Mechanical Advantage
The number of times a machine multiplies your effort force.
Example: If you push on the handle of a car jack with a force of 30 lbs and the jack lifts a 3000 lb car, what is the jack’s mechanical advantage?
The jack multiplies your effort force by 100 times.
Link

14. There are 2 types of mechanical advantage.
IMA – Ideal mechanical advantage.
This is the number of times a machine is designed to multiply your effort force.
Ignores friction
AMA – Actual mechanical advantage
This is the number of times the machine actually multiplies your effort force.
Includes the effects of friction
Frictional forces convert some of the energy to thermal energy
IMA is always larger than AMA.

15. B. Force Input Force (Fi) Output Force (Fo)
force applied to the machine
“what you do”
Output Force (Fo)
force applied by the machine
“what the machine does”

16. Win = Fin × din Wout = Fout × d0ut
C. Work
Work Input (Win)
work done on a machine
Win = Fin × din
Work Output (Wout)
work done by a machine
Wout = Fout × d0ut

17. Fin × din = Fout × dout Win = Wout C. Work Conservation of Energy
can never get more work out than you put in
trade-off between force and distance
Win = Wout
Fin × din = Fout × dout

18. Win = Wout Win > Wout But in the real world…
C. Work
In an ideal machine (no friction)...
Win = Wout
But in the real world…
some energy is transferred to heat due to friction
Win > Wout

19. Fi = ? Win = Wout Fo = 1,500 N Findin = Foutdout Din = 5 cm
Work
A hammer claw moves a distance of 1 cm to remove a nail. If an output force of 1,500 N is exerted by the claw and you move the handle 5 cm, what is your input force?
GIVEN:
Fi = ?
Fo = 1,500 N
Din = 5 cm
D out = 1 cm
WORK:
Win = Wout
Findin = Foutdout
Fin (0.05 m) = (1,500 N) (0.01 m)
Fin (0.05 m) = 15 Nm
Fin = 300 N

20. D. Mechanical Advantage
Mechanical Advantage (MA)
number of times a machine multiplies the effort force
MA > 1 : force is increased
MA < 1 : distance is increased
MA = 1 : only direction is changed

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

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

23. Efficiency
Efficiency – measure of how much of the work put into a machine is changed into useful output work by the machine
High efficiency = less thermal energy from friction and more energy converted to useful output work. (ideally Wout = Win 100% efficient)
How would you increase a machine’s efficiency?
Grease, lubricant

25. There are 3 Classes of Levers
Depends on the location of 3 items:
1. Fulcrum – fixed point on a lever
2. Effort Arm – the part of the lever that exerts the effort force.
3. Resistance Arm – the part of the lever that exerts the resistance force.
 EA 
RA

26. 1st Class Lever Changes the direction of the force
Multiplies effort force
Magnifies speed and distance
Ex: seesaw, crowbar, scissors

27. 2nd Class Lever Multiply effort force
Mechanical advantage is always greater than 1.
Ex: bottle opener, boat oars, wheel barrow

28. 3rd Class Lever Magnifies speed and distance
Mechanical Advantage always less than 1
Ex: baseball bat, golf club, broom, shovel

31. 1. What is the IMA of this pulley system. 2
1. What is the IMA of this pulley system? Ignoring friction, if you want to lift the resistance 3 meters what will the effort distance be? Ignoring friction how much effort force will be necessary to lift a load of 15 newtons? 4. How much work is done?