Video: Calculating Work from Force and Distance

A force of 320 N is continually applied to push a trolley through a supermarket parking lot. If the trolley is pushed for a distance of 15 meters, how much work was done on the trolley?

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Video Transcript

A force of 320 newtons is continually applied to push a trolley through a supermarket parking lot. If the trolley is pushed for a distance of 15 meters, how much work was done on the trolley?

Now the first thing we can say here is that trolley in this case is another word for shopping cart. So we have this cart and weโ€™re pushing it around the parking lot. Weโ€™re told specifically that as we push the cart, weโ€™re applying a force โ€” we can call it ๐น โ€” of 320 newtons. And that thanks to that force being applied to the cart, the cart travels a distance โ€” we can call that distance ๐‘‘ โ€” given as 15 meters. What we want to find out is given this force and given this distance, how much work was done on the cart? To figure this out, letโ€™s recall the relationship that connects work with force and distance.

Under two conditions and weโ€™ll get to what those are in just a second. The work done on an object, ๐‘Š, is equal to the force applied to the object multiplied by the distance that it moves. Now here are those two conditions we mentioned. In order for this equation to be valid, the force ๐น must be a constant force. It canโ€™t vary getting smaller or larger. And the second condition is that the force ๐น and the distance ๐‘‘ that the object travels must be in the same direction. As we look at our scenario, we see that both these conditions are met.

We have a constant force of 320 newtons and the force points in the same direction as our cart moves. This means we can indeed solve for the work done on this cart by multiplying the force applied to it with the distance that it travels. That work done on the cart โ€” we can call it ๐‘Š sub ๐‘ โ€” is equal to the force on the cart, 320 newtons, multiplied by the distance it travels, 15 meters. Since both our force and our distance are already in their SI base units, newtons and meters, respectively, we can simply multiply these two values together with their units to solve for the work in units of joules. When we do, we find that ๐‘Š sub ๐‘ is 4800 joules. Thatโ€™s how much work was performed on this cart.

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