The gain in potential energy is 36250 joules in both cases, calculated by multiplying mass, gravity and height. Gravitational potential energy depends only on vertical height and is completely independent of the path taken.
A student is slowly lifted straight up in an elevator from the ground level to the top floor of a building. Later, the same student climbs the staircase, all the way to the top. Given that the height of the building is h = 72.5 m, acceleration due to gravity is g = 10 m s-2 and student’s mass is m = 50 kg. (i) Find the gain in the potential energy if the student is lifted straight up to the top. (ii) Find the gain in the potential energy when the student climbs the stairs to the same top. (iii) What do you conclude about the dependence of the potential energy on the path taken?
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In (i), potential energy gain equals m g h, which is 50 kg multiplied by 10 m s-2 multiplied by 72.5 m, yielding 36250 J. In (ii), climbing the stairs reaches the same vertical elevation, giving an identical gain of 36250 J. In (iii), we conclude that gravitational potential energy depends solely on initial and final vertical positions, being independent of the path followed.
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