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you can exchange the first kids elevator to him stepping up and down a stone on the floor instead I think? It's not the exact same as the elevator step is moving against him, each one shrinking the step he start to take, but assuming that he by each step lifts himself up, maybe?

Two twin kids are making fun in a shopping centre. One of them is "going up" an escalator that is going down, staying in the same level. His brother takes another escalator that is not working and goes up to the next floor. If the first kid plays on the escalator at the same time that his brother climbs to the next floor, do both expend the same amount of energy?

I've never thought of a satisfactory explanation for the objection to the positive answer: Where that energy goes?

In the other case when the boy is walking up the escalator which is in motion then the boy's muscles are working and the escalator is also doing work.

I look at this way:Ignoring the energy involved in getting to the steady-state condition:You have two boys of identical mass (say 20kg), both walking upwards for (say) 10 secondsOne escalator is stationary, and the boy is gaining altitude at 0.5 m/s.The other escalator is moving, and the boy is not gaining any altitude, but his feet are still moving vertically at 0.5m/s

[/li][li]The average force on the escalator is the same for each boy - about 200 Newtons, averaged over this 10s period.[/li][li]The energy expended is Force x Distance = 200 N x 5m = 1000 J [/li][/list]Including the effort required to get on and off the escalators is left as an exercise for the reader... (Read: "I've had a long day, and I'm going to bed".)

The vertical distance moved by their shoes is 5m in this 10s period

But it is not measurable in this case, there is no way I know of to measure 'potential energy' directly.