A carer does 36 joules of work in
24 seconds to push a baby carriage at a speed of 0.25 metres per second. What average force does the carer
apply on the baby carriage?
Okay, so in this question, we’ve
been told that we’ve got 36 joules of work being done in 24 seconds on a baby
carriage to push it at a speed of 0.25 metres per second. We’ve been asked to find the
average force applied by the carer on the baby carriage for it to move at 0.25
metres per second.
Now, the first thing to do is to
list all of the important quantities given to us in the question. We start by saying that the work
done 𝑊 on the baby carriage is 36 joules. We then say that the time taken for
this work to be done is 24 seconds. Next, we can say that the carriage
is moving at a speed of 0.25 metres per second. And we’re trying to find out the
average force on the carriage.
Now, to do this, let’s first recall
the definition of the work done on an object. The work done on an object 𝑊 is
defined as the average force applied to an object multiplied by the distance moved
by the object whilst the force is applied.
Now, in this case, we’re trying to
work out what the force applied is. And we’ve been given the work done
on the object. However, we don’t know how far the
object moves. In this case of course, the object
is being the baby carriage. However, we have been told how fast
the baby carriage travels and for how long is travelling at this speed.
Therefore, we can recall that the
definition of speed is the distance travelled divided by the time taken for that
distance to be travelled. And we can rearrange this equation
by multiplying both sides of the equation by the time taken 𝑡 so that the time
cancels out on the right-hand side. And we’re left with just the
distance travelled. And hence, the time taken
multiplied by the speed of the object is equal to the distance travelled by the
We can then take this equation and
substitute it instead of the distance travelled. Hence, what we’re left with is that
the work done on the object is equal to the force applied on the object multiplied
by the distance travelled by the baby carriage, which we know to be the time taken
for the baby carriage to travel that distance multiplied by the speed of the baby
At which point, we know all but one
of the quantities in the equation. We know the work done on the baby
carriage, we know the time taken for the baby carriage to travel a certain distance,
and we know the speed of the baby carriage. Also, we’re trying to work out the
force exerted on the baby carriage.
So we just need to rearrange this
equation. We can do this by dividing both
sides of the equation by the time multiplied by the speed so that the time cancels
on the right-hand side and so does the speed. Now, we could have done the same
thing by dividing both sides of the equation by the distance travelled and then
substitute in the distance for the time multiplied by the speed. But it doesn’t really matter which
way around we’ll do it as long as we get the same answer.
So what we’re left with is that the
work done divided by the time taken multiplied by the speed of the baby carriage is
equal to the force applied on the baby carriage. Now, we can substitute in the
values. So the work done is 36 joules, the
time taken is 24 seconds, and the speed is 0.25 metres per second.
Then, we evaluate the fraction on
the left-hand side to give us a value of six. But six what? What are the units? Well, we’ve been working in
standard units so far. For example, the work done is given
in joules, which is its standard unit; the time taken is in seconds, again the
standard unit; and the speed is in metres per second, once again the standard
unit. So our final answer is going to be
in its standard unit, which is the newton because that’s the standard unit of
And hence, we’ve reached our final
answer: the average force applied by the carer to the baby carriage is six