We already know that work equals force times distance. Pretend two guys are lifting weights.
They both lift the same amount, the same distance, but one does it faster than the other. That
mean's one's doing more work, right? Wrong. They are both doing the exact same amount of work.
But how can that be, something needs to be different. True, and that's where power comes in.
Power is equal to work over time. That means that the guy lifting weights faster, while doing
the same work as the slower guy, is exerting more power.
As stated earlier, the equation for power is:
P = W / t
Power is measured in units called Watts. You've heard of a 60 Watt light bulb. The 60 watts
has to do with the amount of power the light bulb is exerting. A Watt is a shortcut for, at the
most basic level, kgm2/s3. But we usually write W or J/s. Let's continue with that weight
lifter situation in our sample problem.
Two weight lifters in a gym are both lifting 50kg worth of weights 0.45m in the air. One of
the weight lifters does 20 repetitions in a minute, while the second weight lifter does 30
repetitions in a minute.
a. How much power is being exerted by the first weight lifter?
b. How much power is being exerted by the second weight lifter?
First, we need to figure out the amount of work they are doing. Since we don't need the
mass of the weights, we need to figure out how we can change them into something useful, like
the force being exerted upon them. We know that the weight lifters are working against gravity,
and the weights are moving at a constant velocity, therefore the force they are exerting must be
equal to the force of gravity. We can find that easily using Newton's Second Law.
F = 50kg * 9.8m/s2
F = 490N
W = 490N * .45m
W = 220.5J
Now that we have that, we need to split it up into parts a and b.
a. we know that 20 reps/min is equal to 3 s/rep.
P = 220.5J / 3s
P = 73.5W
b. we know that 30 reps/min is equal to 2 s/rep.
P = 220.5J / 2s
P = 110.25W
That's all there is to the basics of work and power. Like I said work is only one type of
energy, there are many others some of which we have already discussed. Kinetic energy,
Gravitational energy, Electric energy, etc...
Well, that's all for now, but be sure to check back now and then for updates.
Work, Energy & Power Sample Problems
