### Video Transcript

Which of the following formulas
correctly shows the relationship between the magnitude of a force, the work done by
that force, and the distance moved in the direction of the applied force by the
object that the force is applied to?

Before we review our answer
options, letโs consider whatโs going on in this situation. We have some object. Weโll say that this is our
object. And we imagine that some force is
being applied to this object. We can call that force ๐น. And that along with this, the
object moves or is displaced at some distance โ we can call that ๐ โ in the same
direction as this force ๐น is applied. Based on that, our question is,
which of these five options โ A, B, C, D, or E โ gives us the correct formula,
showing the relationship between these two quantities โ force, distance โ and a
third quantity the work done on our object. In other words, we want to know how
work, force, and distance are related to one another mathematically.

That being said, letโs look at our
answer candidates. A) Work is equal to distance
divided by force. B) Work is equal to force divided
by distance. C) work is equal to distance minus
force. D) Work is equal to force times
distance. E) Work is equal to force minus
distance.

One of the first things we can do
to start narrowing down our answer options is to consider the units involved in
these expressions. Each one of these expressions
involves three terms. Thereโs work, ๐, force, ๐น, and
distance, ๐. Now, if we consider the units of
each of these three terms, work, force, and distance, then starting at the top, the
unit of work is the joule, abbreviated capital ๐ฝ. The base unit for force we know to
be the newton, abbreviated capital ๐. And the base unit for distance or
displacement is the meter.

Now, letโs consider for a moment
that the unit of work is the joule. Looking at these five answer
options, we see that work appears on the left-hand side of each one. And since the unit of work is the
joule, that means the left-hand side of every one of these equations has units of
joules. Now, if some amount of work in
units of joules is equal to some other quantity, that is the quantity on the
right-hand side, then that means the right-hand side of the correct formula must
also be expressed ultimately in these same units, in units of joules. This means that if we can say for
sure that the units on the right-hand side of any of these expressions cannot be
joules, in that case, those answer options cannot be the correct formula.

Keeping this in mind, letโs
consider answer options C and E. Option C claims that work is equal
to distance minus force, where option E claims that work is equal to force minus
distance. We know that the units of force are
newtons, and the units of distance are meters. But that means that weโre not able
to combine the units of these terms in this way and wind up with units of joules,
which we would have to, if they were to agree with the left-hand side. For example, for answer option C,
we would have a distance in meters minus a force in newtons. But subtracting some number of
newtons from some number of meters doesnโt give us some number of joules. The units donโt work out. And this means that answer option C
canโt be our correct formula.

Answer option E drops out for the
same reason. Some number of newtons minus some
number of meters cannot equal some number of joules. So weโre down to answer options A,
B, and D. Now, at this point, we can recall
that there is a relationship that ties together the units of joules, newtons, and
meters. The definition of the unit joule is
that one joule is equal to one newton of force multiplied by one meter of
distance. Written another way, we can say
that a joule is equal to a newton meter. This shows us that whatever our
correct answer option is, weโll have units of newtons multiplied by meters on the
right-hand side of our expression.

Looking at option A, we see that
this candidate has units of meters divided by newtons, so not newtons times meters,
whereas option B has units on the right-hand side of newtons divided by meters. Then, finally, option ๐ has units
on the right-hand side of newtons multiplied by meters. We see that itโs this option which
gives us the units on the right-hand side which agree with the units equivalent to a
joule. Therefore, option D has the correct
relationship between the units on the left-hand and right-hand side. And therefore, this is our choice
for the formula correctly representing the relationship between work, force, and
distance. Work is equal to force multiplied
by distance.