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I came across a question the other day that I couldn't answer. I asked it to everyone I know, including my physics professor, but even he couldn't seem to give an answer, calling this question a red herring. Therefore, I'd like to post it here.

The question (which is only worth 2 marks) states

Point Q is 3 metres above and 4 metres north of point P. How much energy input is required to move a box of 5kg from point P to Q?

I already worked out the energy required to lift the box by the formula:

$$E = mgh = 5 \cdot 9.8 \cdot 3 = 147\mathrm{J}$$

But how do you work out the energy input required to push the box forward? No value of "v" is given, so the kinetic energy formula cannot be used. My professor believes that this is all that can be done - i.e. the only thing you can do is to calculate the energy required to lift the object, and that is the final answer. But is this true? Is the second part of the question just a red herring, with it being impossible to calculate the energy needed to push an object forward?

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2 Answers 2

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Typically a question like this wants to drive home the point that if there is no force opposing the motion (moving "North" presumably means you are "in the air with no friction) then no net work is done in the physics sense.

Of course to actually perform the motion you fist need to accelerate the mass and later decelerate it - but the work done to accelerate it can in principle be recovered during the deceleration (for example by slowing down the mass with a spring so the kinetic energy is turned into elastic energy)

So yes you teacher is right - for a question like this the answer is just $mgh$ and you ignore the horizontal motion unless the question gives information that allows you to compute friction etc.

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One possibility is to search for the minimal required energy: How to trow the box in such a way that the maximum of the parabolic throwing lies at (x,y)=(4,3)? The rest can be read on wikipedia.

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