### Video Transcript

2240 joules of work is done to a
bookcase being pushed by a constant force of 1600 newtons. How far is the bookcase pushed by
the force?

Okay, so let’s imagine that this
here is our bookcase. We are told that this bookcase is
pushed by a constant force of 1600 newtons. Let’s suppose that this force is
acting to the right, and we’ll label it as 𝐹. We’re also told that the work done
by this force is 2240 joules. Let’s label this work done as
𝑊. When this force 𝐹 is applied to
the bookcase, it’s gonna push the bookcase so that it moves to the right. Let’s suppose that the force causes
the bookcase to move to this new position here.

The question is asking us to work
out how far the bookcase is pushed by the force. In other words, we need to find the
distance between where the bookcase starts out and where it ends up, which we’ve
labeled as 𝑑. In order to work this out, we can
recall that there’s an equation which links the work done by a force, the magnitude
of that force, and the distance that an object moves. Specifically, that equation is that
work done is equal to force multiplied by distance.

Alternatively, we can write this in
terms of symbols as 𝑊 is equal to 𝐹 multiplied by 𝑑. In this case, we know the value of
𝑊. That’s the work done by the
force. And we also know the magnitude of
the force 𝐹. The quantity that we don’t know and
that we’re trying to find is the distance moved by the bookcase when the force is
applied. So, let’s take this equation and
rearrange it to make the distance 𝑑 the subject.

To do this, we divide both sides of
the equation by the force 𝐹. On the right-hand side, we have an
𝐹 in the numerator which cancels with the 𝐹 in the denominator. This gives us an equation that says
𝑊 divided by 𝐹 is equal to 𝑑. Of course, we can also write this
equation the other way around to say that the distance moved 𝑑 is equal to the work
done 𝑊 divided by the force 𝐹. This equation then allows us to
calculate the distance moved by the bookcase as long as we know the work done by the
force and the force’s magnitude. Luckily, in this case, we know the
values for both of these two quantities. So, let’s go ahead and sub those
values into this equation.

When we do this, we get that 𝑑 is
equal to 2240 joules, that’s the value for 𝑊, divided by 1600 newtons, the value
for 𝐹. At this point, we can notice that
the work done is expressed in units of joules, the SI base unit for energy, and the
force is in units of newtons, the SI base unit for force. This means that the distance this
expression is going to give us will be in the SI base unit for distance, which is
the meter. Evaluating the expression gives us
a result of 1.4 meters.

So, our answer to the question is
that the distance the bookcase is moved when it’s pushed by the force is 1.4
meters.