Power

Power (physics)From Wikipedia, the free encyclopediaFor other types of power, seePower (disambiguation).Common symbolsP

SIunitwatt

Classical mechanics

Second law of motion

History Timeline

Branches[show]

Fundamentals[show]

Formulations[show]

Core topics[show]

Rotation[show]

Scientists[show]

v t e

Inphysics,poweris the rate of doingwork. It is equivalent to an amount ofenergyconsumed per unit time. In theSI system, the unit of power is thejouleper second (J/s), known as thewattin honor ofJames Watt, the eighteenth-century developer of thesteam engine.Theintegralof power over time defines the work performed. Because this integral depends on the trajectory of the point of application of the force and torque, this calculation of work is said to bepath dependent.As a physical concept, power requires both a change in the physical universe and a specified time in which the change occurs. This is distinct from the concept of work, which is only measured in terms of a net change in the state of the physical universe. The same amount of work is done when carrying a load up a flight of stairs whether the person carrying it walks or runs, but more power is needed for running because the work is done in a shorter amount of time.The output power of an electric motor is the product of thetorquethat the motor generates and the angular velocity of its output shaft. The power involved in moving a vehicle is the product of the traction force of the wheels and the velocity of the vehicle. The rate at which a light bulb converts electrical energy into light and heat is measured in wattsthe higher the wattage, the more power, or equivalently the more electrical energy is used per unit time.[1][2]Contents[hide] 1Units 2Average power 3Mechanical power 3.1Mechanical advantage 4Electrical power 5Peak power and duty cycle 6See also 7ReferencesUnits[edit]

Ansel Adamsphotograph of electrical wires of the Boulder Dam Power Units, 19411942The dimension of power is energy divided by time. TheSIunit of power is thewatt(W), which is equal to onejouleper second. Other units of power includeergsper second (erg/s),horsepower(hp), metric horsepower (Pferdestrke(PS) orcheval vapeur, CV), andfoot-poundsper minute. One horsepower is equivalent to 33,000 foot-pounds per minute, or the power required to lift 550poundsby one foot in one second, and is equivalent to about 746 watts. Other units includedBm, a relative logarithmic measure with 1 milliwatt as reference; (food)caloriesper hour (often referred to askilocaloriesper hour);Btuper hour (Btu/h); andtons of refrigeration(12,000 Btu/h).Average power[edit]As a simple example, burning a kilogram ofcoalreleases much more energy than does detonating a kilogram ofTNT,[3]but because the TNT reaction releases energy much more quickly, it delivers far more power than the coal. If Wis the amount ofworkperformed during a period oftimeof duration t, theaverage powerPavgover that period is given by the formula

It is the average amount of work done or energy converted per unit of time. The average power is often simply called "power" when the context makes it clear.Theinstantaneous poweris then the limiting value of the average power as the time interval tapproaches zero.

In the case of constant powerP, the amount of work performed during a period of durationTis given by:

In the context of energy conversion, it is more customary to use the symbolErather thanW.Mechanical power[edit]Power in mechanical systems is the combination of forces and movement. In particular, power is the product of a force on an object and the object's velocity, or the product of a torque on a shaft and the shaft's angular velocity.Mechanical power is also described as the time derivative of work. Inmechanics, theworkdone by a forceFon an object that travels along a curveCis given by theline integral:

wherexdefines the pathCandvis the velocity along this path.If the forceFis derivable from a potential (conservative), then applying thegradient theorem(and remembering that force is the negative of thegradientof the potential energy) yields:

whereAandBare the beginning and end of the path along which the work was done.The power at any point along the curveCis the time derivative

In one dimension, this can be simplified to:

In rotational systems, power is the product of thetorqueandangular velocity,

wheremeasured in radians per second. Therepresentsscalar product.In fluid power systems such as hydraulic actuators, power is given by

wherepispressureinpascals, or N/m2andQisvolumetric flow ratein m3/s in SI units.Mechanical advantage[edit]If a mechanical system has no losses, then the input power must equal the output power. This provides a simple formula for themechanical advantageof the system.Let the input power to a device be a forceFAacting on a point that moves with velocityvAand the output power be a forceFBacts on a point that moves with velocityvB. If there are no losses in the system, then

and themechanical advantageof the system (output force per input force) is given by

The similar relationship is obtained for rotating systems, whereTAandAare the torque and angular velocity of the input andTBandBare the torque and angular velocity of the output. If there are no losses in the system, then

which yields themechanical advantage

These relations are important because they define the maximum performance of a device in terms ofvelocity ratiosdetermined by its physical dimensions. See for examplegear ratios.Electrical power[edit]Main article:Electric powerThe instantaneous electrical powerPdelivered to a component is given by

whereP(t) is the instantaneous power, measured inwatts(joulespersecond)V(t) is thepotential difference(or voltage drop) across the component, measured involtsI(t) is thecurrentthrough it, measured inamperesIf the component is aresistorwith time-invariantvoltagetocurrentratio, then:

where

is theresistance, measured inohms.Peak power and duty cycle[edit]

In a train of identical pulses, the instantaneous power is a periodic function of time. The ratio of the pulse duration to the period is equal to the ratio of the average power to the peak power. It is also called the duty cycle (see text for definitions).In the case of a periodic signalof period, like a train of identical pulses, the instantaneous poweris also a periodic function of period. Thepeak poweris simply defined by:.The peak power is not always readily measurable, however, and the measurement of the average poweris more commonly performed by an instrument. If one defines the energy per pulse as:

then the average power is:.One may define the pulse lengthsuch thatso that the ratios

are equal. These ratios are called theduty cycleof the pulse train.See also[edit] Simple machines Mechanical advantage Motive power Orders of magnitude (power) Pulsed power Intensity in the radiative sense, power per area Power gain for linear, two-port networks. Power density Signal strength Sound powerReferences[edit]1. Jump up^Halliday and Resnick (1974). "6. Power".Fundamentals of Physics.2. Jump up^Chapter 13, 3, pp 13-2,3The Feynman Lectures on PhysicsVolume I, 19633. Jump up^Burning coal produces around 15-30megajoulesper kilogram, while detonating TNT produces about 4.7 megajoules per kilogram. For the coal value, seeFisher, Juliya (2003)."Energy Density of Coal".The Physics Factbook. Retrieved30 May2011.For the TNT value, see the articleTNT equivalent. The coal value does not include the weight of oxygen used during combustion, while the TNT number if TNT only.[hide] v t eClassical mechanics derived SI units

Linear/translational quantitiesAngular/rotational quantities

time:tstime:ts

displacement,position:xmangular displacement,angle:rad

frequency:fs1, Hzspeed:v,velocity:vm s1frequency:fs1, Hzangular velocity:rads1

acceleration:am s2angular acceleration:rads2

jerk:jm s3angular jerk:rads3

mass:mkgmoment of inertia:Ikgm2rad2

momentum:p,impulse:Jkgm s1,N sangular momentum:L,angular impulse:Lkgm2s1rad1

force:F,weight:Fgkgm s2, Nenergy:E,work:Wkgm2s2, Jtorque:,moment:Mkgm2s2rad1, N menergy:E,work:Wkgm2s2, J

yank:Ykgm s3, N s1power:Pkgm2s3,Wrotatum:Pkgm2s3rad1power:Pkgm2s3,W

Categories: Concepts in physics Power (physics)