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Power
Suppose that an object moves in a general forcefield
.
We now know how to calculate how much energy flows from the forcefield
to the object as it moves along a given path between two
points. Let us now consider the rate at which this energy flows.
If is the amount of work that the forcefield performs on the mass
in a time interval then the rate of working is given by

(176) 
In other words, the rate of workingwhich is usually referred to as the
poweris simply the time derivative of the work performed.
Incidentally, the mks unit of power is called the watt (symbol W). In
fact, 1 watt equals 1 kilogram metersquared per secondcubed, or
1 joule per second.
Suppose that the object displaces by in the time interval
. By definition, the amount of work done on the object
during this time interval is given by

(177) 
It follows from Eq. (176) that

(178) 
where
is the object's instantaneous velocity.
Note that power can be positive or negative, depending on the relative
directions of the vectors and . If these
two vectors are mutually perpendicular then the power is zero.
For the case of 1dimensional motion, the above expression reduces to

(179) 
In other words, in 1dimension, power simply equals force times velocity.
Next: Worked example 5.1: Bucket
Up: Conservation of energy
Previous: Motion in a general
Richard Fitzpatrick
20060202