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 which 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.

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. For historical reasons, the
horsepower is occasionally used to describe the power
delivered by a machine. One horsepower is equivalent to
approximately 750 Watts.

Most machines are designed and built to do
work on objects. All machines are typically described by a
power rating. The power rating indicates the rate at which
that machine can do work upon other objects. Thus, the power
of a machine is the work/time ratio for that particular
machine.
A car engine is an example of a machine which is given a
power rating. The power rating relates to how rapidly the
car can accelerate the car. Suppose that a 40-horsepower
engine could accelerate the car from 0 mi/hr to 60 mi/hr in
16 seconds. If this were the case, then a car with four
times the horsepower could do the same amount of work in
one-fourth the time. That is, a 160-horsepower engine could
accelerate the same car from 0 mi/hr to 60 mi/hr in 4
seconds. The point is that for the same amount of work,
power and time are inversely proportional. The power
equation suggests that a more powerful engine can do the
same amount of work in less time.

A person is also a machine which has a
power rating. Some people are more power-full than
others. That is, some people are capable of doing the same
amount of work in less time or more work in the same amount
of time. A common physics lab involves quickly climbing a
flight of stairs and using mass, height and time information
to determine a student's personal power. Despite the
diagonal motion along the staircase, it is often assumed
that the horizontal motion is constant and all the force
from the steps are used to elevate the student upward at a
constant speed. Thus, the weight of the student is equal to
the force which does the work on the student and the height
of the staircase is the upward displacement. Suppose
that Ben Pumpiniron elevates his 80-kg body up the 2.0 meter
stairwell in 1.8 seconds. If this were the case, then we
could calculate Ben's power rating. It can be assumed
that Ben must apply a 800-Newton downward force upon the
stairs to elevate his body. By so doing, the stairs would
push upward on Ben's body with just enough force to lift his
body up the stairs. It can also be assumed that the angle
between the force of the stairs on Ben and Ben's
displacement is 0 degrees. With these two approximations,
Ben's power rating could be determined as shown below.

Ben's power rating is 871 Watts. He is quite a
horse.

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.

This new equation for power reveals that a
powerful machine is both strong (big force) and fast (big
velocity). A powerful car engine is strong and fast. A
powerful piece of farm equipment is strong and fast. A
powerful weightlifter is strong and fast. A powerful linemen
on a football team is strong and fast. A machine
which is strong enough to apply a big force to cause a
displacement in a small mount of time (i.e., a big velocity)
is a powerful machine.

Check
Your Understanding

Use your understanding of work and power to answer the
following questions. When finished, click the button to view
the answers.

1.
Two physics students, Will N. Andable and Ben Pumpiniron,
are in the weightlifting room. Will lifts the 100-pound
barbell over his head 10 times in one minute; Ben lifts the
100-pound barbell over his head 10 times in 10 seconds.
Which student does the most work? ______________ Which
student delivers the most power? ______________ Explain your
answers.

2. During a physics lab, Jack and Jill ran up a hill.
Jack is twice as massive as Jill; yet Jill ascends the same
distance in half the time. Who did the most work?
______________ Who delivered the most power? ______________
Explain your answers.

3.
A tired squirrel (mass of approximately 1 kg) does push-ups
by applying a force to elevate its center-of-mass by 5 cm in
order to do a mere 0.50 Joule of work. If the tired squirrel
does all this work in 2 seconds, then determine its
power.

4.
When doing a chin-up, a physics student lifts her
42.0-kg body a distance of 0.25 meters in 2 seconds. What is
the power delivered by the student's biceps?

5. Your household's monthly electric bill is often
expressed in kilowatt-hours. One
kilowatt-hour is the
amount of energy delivered by the flow of l kilowatt of
electricity for one hour. Use conversion factors to show how
many joules of energy you get when you buy 1 kilowatt-hour
of electricity.

6. An escalator is used to move 20 passengers every
minute from the first floor of a department store to the
second. The second floor is located 5.20 meters above the
first floor. The average passenger's mass is 54.9 kg.
Determine the power requirement of the escalator in order to
move this number of passengers in this amount of time.