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