The quantity work has to do with a force
causing a displacement. Work has nothing to do with the amount of time that
this force acts to cause the displacement. Sometimes, the work is done very
quickly and other times the work is done rather slowly. For example, a rock
climber takes an abnormally long time to elevate her body up a few meters along
the side of a cliff. On the other hand, a trail hiker (who selects the easier
path up the mountain) might elevate her body a few meters in a short amount of
time. The two people might do the same amount of work, yet the hiker does the
work in considerably less time than the rock climber. The quantity that has to
do with the rate at which a certain amount of work is done is known as the
power. The hiker has a greater power rating than the rock
climber.
Power is the rate at which work
is done. It is the work/time ratio. Mathematically, it is computed using the
following equation.
Power = Work / time
or
P = W / t
The standard metric unit of power is the Watt. As is
implied by the equation for power, a unit of power is equivalent to a unit of
work divided by a unit of time. Thus, a Watt is equivalent to a Joule/second
The expression for power
is work/time. And since the expression for work is force * displacement, the
expression for power can be rewritten as (force * displacement) / time. Since
the expression for velocity is displacement / time, the expression for power
can be rewritten once more as force * velocity. This is shown below.
Power = Work/Time = (Force * Displacement)/Time
Power = Force * (Displacement/Time)
Power = Force * Velocity
This new equation for power
reveals that a powerful machine is both strong (big force) and fast (big
velocity).
Example
1:
An elevator can
carry a maximum load of 1800 kg (elevator + passengers) is moving up with a
constant speed of 2 ms–1. The frictional force opposing the motion is 4000 N. Determine
the minimum power delivered by the motor to the elevator in watts as well as in
horse power.
Solution:
The downward force on the elevator is
F = mg + Ff = (1800 × 10) + 4000 = 22000 N
The motor must supply enough power to balance this force. Hence,
P = F.v = 22000 × 2 = 44000W = 59 hp
The downward force on the elevator is
F = mg + Ff = (1800 × 10) + 4000 = 22000 N
The motor must supply enough power to balance this force. Hence,
P = F.v = 22000 × 2 = 44000W = 59 hp
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