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?
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.
