Video Transcript
Which of the following formulas
correctly shows the relationship between the time taken to do an amount of work and
the power supplied to do the work? A) Power equals time divided by
work. B) Power equals work times
time. C) Power equals work minus
time. D) Power equals work divided by
time. E) Power equals work plus time.
We’re told that these five options
are all candidates for the correct formula showing the relationship between the time
taken to do an amount of work and the power supplied to do it. We’re working then with these three
particular quantities, power, work, and time. Now even if we don’t have the exact
relationship between these three terms committed to memory, if we’re able to recall
the units of these three terms, we’ll be able to narrow down our answer options.
Starting from the bottom, the SI
base unit of time is the second, abbreviated s. The unit for work is the joule,
abbreviated capital J. And, notice, that this is the same
as the unit for energy. And then, lastly, the SI unit for
power is the watt, abbreviated capital W.
As we consider our answer options,
we know that whichever one is correct will have the same units on either side of the
equality sign. That’s part of what makes it an
equation. And since we know that the SI unit
of power is the watt, we realize that all five of our options will have that unit on
the left-hand side of the equality, which means that whichever answer option is
correct must have that same unit, the watt, on the right-hand side.
As we consider answer options C and
E, we see that the right-hand side will not have those units for these two
choices. For these two choices, what we have
on the right-hand side is a mixture of units. The work has units of joules and
the time has units of seconds. In each of these cases then, we’re
not able to perform the operation on the right-hand side. We’re not comparing quantities of a
similar type to one another. From a units perspective then, we
can say that options C and E are out of the running. The final unit on the right-hand
side of these expressions can’t possibly be watts. And so, it can’t be a correct
formula.
That leaves A, B, and D. At this point, it’ll be helpful to
us to recall the definition of power. Power is defined as energy
transferred per unit time. In other words, it’s an amount of
energy in units of joules divided by an amount of time in units of seconds. And note that this energy transfer
can be happening thanks to the work done by some entity. We could equally well define power
as work done per unit time.
So, the unit of work, as we saw, is
the joule. And the base unit of time is the
second. And our definition for power is
telling us that power is an amount of energy in joules per amount of time in
seconds. To answer our question then, we’ll
go through answer options A, B, and D and see which one has units of joules per
second on the right-hand side.
Let’s start out by testing answer
option A. On the right-hand side of this
equation, we have a time in units of seconds divided by work, which has units of
joules. That’s not an overall unit of
joules per second. So, we’ll cross out option A. Moving on to option B, this
right-hand side has work done in units of joules multiplied by time in units of
seconds. The unit here is a joule times
second rather than a joule per second, so option B is also off the table.
Lastly, we get to option D, where
we have work done in joules divided by time in seconds. Here, we have a match for the units
we were looking for, a match for the units of power. We can say then that a joule per
second is equal to a watt, the unit of power. And this makes option D the correct
choice. Power is equal to work divided by
time.
