Does Bus Travel Affect the Boy's P.E.?

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When a boy travels by bus up a mountain, he gains gravitational potential energy (G.P.E.) as his distance from the Earth's center increases. This increase in G.P.E. can be calculated using the formula P_e = mgh, where 'm' is the total mass of the bus and passengers. Conversely, as the bus descends, the boy loses G.P.E. while his kinetic energy becomes part of the bus's overall energy. The boy's energy changes are directly tied to the bus's motion and elevation. Thus, bus travel does affect the boy's potential energy during the journey.
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A boy travels by bus. When it goes up a mountain, does the boy inside the bus gain in P.E.? Vice versa, does he loss in P.E. when the bus goes down? :confused:
 
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Yes he gains G.P.E. as we can simply think of his G.P.E. as a function of his distance from the centre of the Earth.
 
As the bus is in motion up the hill. The boy can be thought of as part of the bus.
P_e = mgh
the mass is the total mass of the bus and the passengers. Same with the bus going down the hill. The kinetic energy of the boy becomes part of the bus.
 
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