Video: Calculating Force given the Work Done

A carer does 36 J of work in 24 s to push a baby carriage at a speed of 0.25 m/s. What average force does the carer apply on the baby carriage?

03:33

Video Transcript

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 object.

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 carriage.

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 force.

And hence, we’ve reached our final answer: the average force applied by the carer to the baby carriage is six newtons.

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