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Power
The rate at which work is done.
Objective: To define and apply the concepts of power and mechanical efficiency.
The power is the work done divided by the time it takes to do the work.
t
WP
Units:
J/s = Watt
1 horsepower =746 Watts
1000 Watts = 1 kW
Kilowatt-hours (kwh) measure energy.
Jss
Jkwh 6106.3360010001
SRP charges about 10 cents for 1kwh. How much would it cost to leave a 60W light bulb on for a full day?
kWW 060.060
)24)(060.0( hourskW
kWh44.1
centskwh
centskwh 4.14
1044.1
Leaving a 60W light bulb on for 24 hours will cost about 15 cents.
This equation can be written in another form:
t
WP
t
xFP
cos
cosxFxFW
cosFvP
Which has more power?
A 60kg man takes 5 seconds to run up a set of stairs at a constant velocity. What was the man’s power?
t
U
t
WP g
t
mgh
15m
Mass = 60kg
Work is transferred to gravitational potential Energy
5
)15)(10)(60(
)(1800 Wattss
J
A man pushes a 12kg crate horizontally with a constant velocity of 2m/s. The coefficient of friction between the crate and the floor is 0.25. What power does the man have as he pushes the crate? cosFvP
)1)(2)((FP
-120N
120N
Ff
Nf
f
Ff
30
)120)(25(.
)1)(2)(30(P
WP 60
A crane hoist lifts a load of 1000kg a vertical distance of 25m in 9.0s at a constant velocity. What is the useful power output of the crane?
t
mgh
t
U
t
WP g
WP 4108.29
)25)(10)(1000(
If the hoist motor of the previous crane is rated at 70hp, what percentage of this power goes to useful work?
Whp
whp 4102.5
1
74670
W
W4
4
102.5
108.2%
%54
Efficiency – A measure of what you get out for what you put in.
in
out
E
W
inputenergy
outputwork
The Efficiency of a typical car is about 25%!
The motor of an electric drill with an efficiency of 80% has a power of input of 600 W. How much useful work is done by the drill in a time of 30 seconds?
Jss
JW 18000)30(600600
in
out
E
W
inputenergy
outputwork
1800080.0 outW
JWout 14400
A fork lift raises a 120kg load a distance of 3 meters in a time of 8 seconds. What is the power of the fork lift in raising the load? During this process 7600 J of energy is transferred to internal energy. What is the efficiency of the fork lift?
3 m
