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I am sure that I am missing something obvious here. It might have to do with the fact that force is more explicitly defined as the derivative of momemtum. Anyway, can anyone explain why the following example seems to violate one of the two equations for work? (thanks in advance)

eq 1. Work = force * displacement

eq 2. Work = change in kinetic engery

Here is the example:

I have a 747 and a matchbox car in a frictionless environment. Let's say the 747 weighs about 1 million pounds, and the toy car weighs about 1 ounce. (Exact weights, masses, conversions, etc are not necessary for this qualitative example.)

If I apply a force of 1 Newton to each of them for 1 second, the change in kinetic energy of each of them will be the same, but the change in displacement will be vastly different. If I then divide by 1 to get power, I am left to believe that the power to create a 1 newton force varies dramatically in these two cases. Is this becase it is more difficult to maintain a 1 newton force on the toy because it is accelerating so much faster?

I know if I turn the problem around and try to determine how much power is required to accelerate each of them at a certain rate or propel them across a given displacement over a given function of time, the power required works out exactly as I would expect.

Also, I know that if I apply a given force to an object that ends up moving in the opposite direction of my applied force, that I actually do negative work on the object, and so a negative amount of power is required (in other words, I can extract power from the system). I have a feeling that something along these lines has caused me to missunderstand "work = force * displacement"; however, the exact problem with my example is not clear to me.

I am just trying to get an intuitive feel for the concept.

Thanks,

-Mark

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# Work = force * displacement

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