Power, Efficiency, and Machines

PhysicsIn this lesson, we will discuss the

following:

Power

Efficiency

Machines

Definition of Power

Power is defined as how quickly work is done.

Abbreviation for Power

Power is abbreviated P.

P

Formula for Power

Power is equal to work divided by time.

t

WP

And, work is equal to change in energy.

t

EP

SI Units for Power

The SI unit for power is the Watt (W).

s

JW

1

11

1 Joule

1 second

Power is a Scalar Quantity

Power, like work and energy, is a scalar quantity. In other words, power has a magnitude and a unit. Power does NOT have a direction.

Using Power, Work, and Time in Calculations

Problem: What is the power of a light bulb which does 216,000 Joules of work in one hour?

Solution:

WP

s

JP

hour

JP

t

WP

60

3600

000,2161

000,216

Using Power, Work, and Time in Calculations

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Definition of Efficiency

Efficiency is defined as the percentage of useful energy you get out of a machine.

Abbreviation for Efficiency

Efficiency is abbreviated ε.

Lower

-case

epsil

on.

Formula for Efficiency

The efficiency of a machine is equal to useful work you get out of the machine divided by the work put into the machine times 100%.

%100in

out

W

W

Formula for Efficiency

Or, the efficiency of a machine is equal to useful energy you get out of the machine divided by the energy put into the machine times 100%.

%100in

out

E

E

Efficiency is Dimensionless

Efficiency is a dimensionless quantity. In other words, efficiency has no unit(s), unless you call percent a unit. I don’t.

Efficiency is a Scalar Quantity

Efficiency is a scalar quantity. In other words, it has no direction.

Using Efficiency in Calculations

Problem: What is the efficiency of a car which puts out 300 J of energy for every 1000 J of energy it uses?

Solution:

%30

%1001000

300

%100

J

J

E

E

in

out

Using Efficiency in Calculations

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Machines and the Law of Conservation of Energy

All machines must follow the Law of Conservation of Energy. In other words, the energy that is put into a machine is always at least as large as the useful energy that is taken out of the machine.

In addition, the work that is put into any machine is always at least as large as the useful work that is taken out of the machine.

Machines and the Law of Conservation of Energy

If a machine is 100% efficient, the work put into a machine is exactly equal to the useful work that is taken out of a machine.

Workin = Workout

(Forcein) x (Distancein) = (Forceout) x (Distanceout)

If yo

u w

ant t

o pu

t a

smal

l for

ce in

to a

m

achi

ne…

Then

you

mus

t

exer

t tha

t sm

all

forc

e ov

er a

long

dist

ance

…And if you w

ant to

get out a larger

force…

And only get a small

distance out.

Machines and the Law of Conservation of Energy

Workin = Workout

(Forcein) x (Distancein) = (Forceout) x (Distanceout)

A car jack follows the Law of Conservation of

Energy. A small force put into the jack exerted over a long distance results in a force large enough to pick up a car but over a

very small distance.

Six Examples of Simple Machines

Below you will find six examples of simple machines:

1. Lever2. Inclined Plane3. Wheel and Axle4. Screw5. Wedge6. Pulley

All of these machines follow the

Law of Conservation of Energy!

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Six Examples of Simple Machines

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Six Examples of Simple Machines

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page at the right does not

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