Question Video: Calculating the Force That Does a Given Amount of Work Physics • 9th Grade

A force does 480 J of work pushing an object 32 m. What is the magnitude of the force?

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Video Transcript

A force does 480 joules of work pushing an object 32 meters. What is the magnitude of the force?

So, in this question, we have some object that we’ll draw as this box here. We are told that there’s a force acting on the object and that this causes the object to move a distance of 32 meters. Let’s suppose that this force is acting to the right, and we’ll label it as 𝐹. This force will then cause the object to move to the right, so we can draw it in its new position here, which is a distance of 32 meters away from where it started. We’ve labeled this distance as 𝑑. The other piece of information that we’re given in the question is that the work that is done by the force is equal to 480 joules. Let’s label this work done as 𝑊.

Now, we’ve been asked to find the magnitude of the force, so that’s the value of the quantity we’ve labeled 𝐹. To do this, we can recall that the work done on an object by a force is equal to the magnitude of the force multiplied by the distance moved by the object. We can also write this in terms of symbols as work done 𝑊 is equal to force 𝐹 multiplied by distance 𝑑. In this case, we know the value of the work done, and we know the distance moved by the object. The quantity that we don’t know and that we’re trying to find is the value of the force 𝐹. So we need to take this equation and rearrange it to make 𝐹 the subject.

To do this, we divide both sides of the equation by the distance 𝑑. Then, on the right-hand side, we have the 𝑑 in the numerator which cancels with the 𝑑 in the denominator. This gives us an equation that says 𝑊 divided by 𝑑 is equal to 𝐹. And of course, we can also write this the other way around to say that the force 𝐹 is equal to the work done 𝑊 divided by the distance 𝑑.

Now, we just need to take our values for the quantities 𝑊 and 𝑑 and sub them into this equation to calculate the value of the force 𝐹. When we do this, we get an equation that says 𝐹 is equal to 480 joules, that’s the value for 𝑊, divided by 32 meters, the value for 𝑑. We can notice that the work done is expressed in units of joules, the SI base unit for energy. And the distance is expressed in units of meters, the SI base unit for distance. This means that the force we’re going to calculate from this equation will be in the SI base unit for force, which is the newton. When we evaluate the expression, we get a result of 15 newtons.

So our answer to this question is that the magnitude of the force acting on the object is 15 newtons.

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