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enter image description here Say a person applies 1 N to a box with a mass of 1 kg, displacing 1 m. This is one Joule of work (1 N for 1 m).

Now say the person applies 1 N to a box with double the mass, displacing 1 m as well. This is still one Joule of work, despite the person having to push with the same amount of force for longer.

So the person expended more energy (pushing with the same effort for longer), but does the same amount of "work". How can the joule be used to measure energy then?

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  • $\begingroup$ That's actually a good (biology) question. But note that energy is defined to be the ability to do work. Some abilities can be wasted, even though they are indeed abilities. $\endgroup$
    – Trebor
    Commented Nov 28, 2022 at 13:48
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    $\begingroup$ Closely related, though not strictly the same question: Why does holding something up cost energy while no work is being done? $\endgroup$
    – Michael Seifert
    Commented Nov 28, 2022 at 13:52
  • $\begingroup$ Your premises are poorly defined. Is there friction involved? If so, you have to do twice as much work on the 2 kg box to displace it a given distance because you have to overcome twice the friction force when compared to the 1 kg box. If you draw a free body diagram, you will see what I mean. $\endgroup$
    – David White
    Commented Nov 28, 2022 at 20:42

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Work is a transfer of energy from one system to another (by any means other than heat). So it must have the same units as energy.

Similarly, if I transfer 5 EUR to your account then your account balance is 5 EUR larger. The transfer is work, and the balance is energy. They must be in the same units. It wouldn't make sense to maintain a balance in EUR but do transfers in liters.

So the person expended more energy (pushing with the same effort for longer), but does the same amount of "work". How can the joule be used to measure energy then?

In your example never use human beings to figure out work and energy. We are marvelously inefficient machines. Instead use an ideal spring or something similar. Two springs in your example would use the same energy. Yes, it would take longer for the spring in B to move the block, but the energy expended would be identical. The spring would operate at a lower power for a longer time.

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  • $\begingroup$ What if I used a rocket instead of a person? The rocket will burn more fuel, and thus expend more energy, yet the same amount of work is done. So again, how can the joule be used to measure work and energy? Your explanation using currency makes complete sense, but I can't seem to be able to put it into practice. I suppose the part I really don't understand is what distance has anything to do with energy. $\endgroup$
    – DaPlaneNerd
    Commented Nov 28, 2022 at 17:54
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    $\begingroup$ With the rocket you are neglecting the energy in the exhaust. That is the usual mistake people make when they use conservation of energy with a rocket. If you include the energy in the exhaust then you will see that it balances out correctly. A spring is easier, don't make things more difficult than necessary. $\endgroup$
    – Dale
    Commented Nov 28, 2022 at 18:54

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