A force of 320 newtons is
continually applied to push a trolley through a supermarket parking lot. If the trolley is pushed for a
distance of 15 meters, how much work was done on the trolley?
Now the first thing we can say here
is that trolley in this case is another word for shopping cart. So we have this cart and we’re
pushing it around the parking lot. We’re told specifically that as we
push the cart, we’re applying a force — we can call it 𝐹 — of 320 newtons. And that thanks to that force being
applied to the cart, the cart travels a distance — we can call that distance 𝑑 —
given as 15 meters. What we want to find out is given
this force and given this distance, how much work was done on the cart? To figure this out, let’s recall
the relationship that connects work with force and distance.
Under two conditions and we’ll get
to what those are in just a second. The work done on an object, 𝑊, is
equal to the force applied to the object multiplied by the distance that it
moves. Now here are those two conditions
we mentioned. In order for this equation to be
valid, the force 𝐹 must be a constant force. It can’t vary getting smaller or
larger. And the second condition is that
the force 𝐹 and the distance 𝑑 that the object travels must be in the same
direction. As we look at our scenario, we see
that both these conditions are met.
We have a constant force of 320
newtons and the force points in the same direction as our cart moves. This means we can indeed solve for
the work done on this cart by multiplying the force applied to it with the distance
that it travels. That work done on the cart — we can
call it 𝑊 sub 𝑐 — is equal to the force on the cart, 320 newtons, multiplied by
the distance it travels, 15 meters. Since both our force and our
distance are already in their SI base units, newtons and meters, respectively, we
can simply multiply these two values together with their units to solve for the work
in units of joules. When we do, we find that 𝑊 sub 𝑐
is 4800 joules. That’s how much work was performed
on this cart.