# Question Video: Calculating the Distance Moved When Work Is Done by a Force Physics • 9th Grade

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

03:11

### 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.

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