A ladder that stands vertically
upward is used by firefighters to reach high windows in a burning building. The ladder is 25 meters long and a
firefighter standing on a ladder 20 meters from its base. The firefighter leans horizontally
to reach into a window beside the ladder, pulling horizontally on the ladder with a
force of 35 newtons. What magnitude of torque is
produced about the base of the ladder when the firefighter leans?
Okay, to answer this question, we
should start by first drawing a diagram. So here’s the ladder that’s
standing vertically and we know that it’s 25 meters long. And here is the firefighter on the
ladder leaning over to reach a window that’s beside the ladder. And we know that he’s a firefighter
because he’s got his protective hat here. And we also know that the
firefighter is standing 20 meters from the base of the ladder.
Now, finally, we’ve been told that
because the firefighter is leaning over, he’s exerting a force of 35 newtons
horizontally on the ladder. And we need to work out the torque
produced about the base of the ladder. Now, a torque is defined as the
force exerted on an object multiplied by the perpendicular distance to the point at
which it acts. And in this case, the 35-newton
force is the force in question. And since we’re taking the torque
about the base of the ladder, the distance between the base of the ladder and where
the force acts is this distance here, which is 20 meters.
So we also know the value of 𝑑,
which means that we can work out the torque or specifically the magnitude or size of
the torque. When we sub in the values, we find
that the torque is equal to the force which is 35 newtons multiplied by the
perpendicular distance which is 20 meters which evaluates to 700 newton meters.
Now at this point, we might be
wondering why we were given the length of the ladder at all. We were told that it is 25 meters
long. Well, the answer to that question
is that it’s actually not relevant. It’s one of those red herring
pieces of information that we need to look at very carefully and sort through when
answering this question. Because remember the perpendicular
distance 𝑑 is defined as the distance between the point at which the force acts and
the point at which the torque is produced — so this distance here. And so in this case, the length of
the ladder is irrelevant.
So at this point, we have our final
answer. The magnitude of the torque
produced about the base of the ladder when the firefighter leans is 700 newton