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power (Definition)

Power

Power is the rate of energy transfer. Since there are several forms of energy, there are several ways of describing power. In general terms of energy, power is defined as

$\displaystyle P = \frac{dE}{dt}.$

Mechanical Power

The energy transfer in mechanical systems where work is done by an applied force

$\displaystyle P = \frac{dE}{dt} = \frac{dW}{dt}.$

Using the relation between work and force

$\displaystyle dW = {\bf F} \cdot d{\bf r}$

and then differentiating to get power,

$\displaystyle P = \frac{dW}{dt} = {\bf F} \cdot \frac{d{\bf r}}{dt} = {\bf F} \cdot {\bf v}.$

The corresponding form of power in rotation is

$\displaystyle P = {\bf M} \cdot {\bf\omega},$

where $ {\bf M}$ is the torque and $ {\bf\omega}$ the angular velocity vector.

Electrical Power

Since energy is transfering from a device storing electrical energy to another device in the circuit that converts to another form of energy, power is the rate of change of electrical potential energy. For a DC circuit

$\displaystyle P = \frac{dU}{dt} = i V.$

Units

The SI unit of the power is one joule per second, which is called watt:

$\displaystyle \frac{\mathrm{J}}{\mathrm{s}} := \mathrm{W}.$

The watt is equal to $ \mathrm{kg \cdot m^2/s^3}$ in the base units.

The english units of power are

$\displaystyle 1 \left [horsepower \right] = 1 \left [hp \right] = 550 \left [\frac{ft \, lb}{s} \right]$


1 joule/second = 1 watt
1,000 watts = 1 kilowatt
746 watts = 1 horsepower
550 ft-lb/sec = 1 horsepower
33,000 ft-lb/min = 1 horsepower

Bibliography

1
Frye, Royal M., Applied Physics. Prentice-Hall, Inc., New York, 1947.



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"power" is owned by bloftin. [ full author list (2) ]
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example of mechanical power (Example) by bloftin
velocity of wave (Definition) by pahio

Cross-references: vector, velocity, relation, work, systems
There are 38 references to this object.

This is version 6 of power, born on 2006-11-16, modified 2006-11-19.
Object id is 235, canonical name is Power.
Accessed 1352 times total.

Classification:
Physics Classification40. (ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS)
 45. (Classical mechanics of discrete systems)
 45.20.Dd (Newtonian mechanics)

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Discussion
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titles or Titles by pahio on 2006-11-18 17:00:58
What is the right procedure for capitalization in the titles of the entries?
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