Say a person stands on the escalator which is going downwards. The normal force by the escalator does negative work, and the gravity does positive work. The person apparently loses some potential energy. What is the effect of the escalator's work on the person's potential energy,from the work-energy theorem perspective? I understand gravity affects the potential energy but I am not sure how the escalator affects if at all.
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1$\begingroup$ Why not try to work it out yourself using the work-energy theorem? If you could explain what part of that you don't understand, maybe we could offer a better answer to your question. $\endgroup$– d_bCommented Sep 4, 2022 at 0:49
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$\begingroup$ My confusion is on the work-energy theorem itself. Does the gravity and escalator's work cancel out, because one does positive work and another does negative work? If cancelled out, what is responsible for the person's potential energy? Maybe I am missing something obvious but I honestly do not know. $\endgroup$– Curious GeorgeCommented Sep 4, 2022 at 0:57
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The work-energy theorem says \begin{align} W_{\text{net}} = \Delta K \end{align} If the only forces exerted on a person on an escalator are gravity and the force exerted by the escalator, then $W_{\text{net}} = W_g + W_e$. If we assume the person moves at constant speed while on the escalator, then $\Delta K = 0$, and \begin{align} W_e + W_g = 0. \end{align} The work done by gravity can be written as minus the change in the gravitational potential energy, so \begin{align} W_e + W_g &= W_e - \Delta U_g =0\\ \rightarrow &\Delta U_g = W_e \end{align} The escalator does work on the system of the Earth and the escalator passenger, storing or extracting gravitational potential energy.
