A hiker with total mass (including gear) of 80 kg starts at a base camp located at an…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A hiker with total mass (including gear) of 80 kg starts at a base camp located at an altitude of 1 600 m above sea level. The hiker follows a long, meandering trail to reach the summit of a mountain at 2 400 m. After resting, the hiker descends by a different, steeper trail that returns to the original base camp.
Assume the only forces that do appreciable work on the hiker during the trip are (i) the gravitational force exerted by Earth and (ii) the normal (contact) force exerted by the ground on the hiker’s boots, which at every instant is perpendicular to the hiker’s instantaneous motion. Neglect all forms of friction and air resistance.
(a) Identify whether the net work done on the hiker by Earth’s gravitational force for the entire round-trip hike is positive, negative, or zero. Explain your reasoning without performing a numerical calculation.
(b) Identify whether the net work done on the hiker by the ground’s normal force for the entire round-trip hike is positive, negative, or zero. Clearly justify your answer by referring to the relative orientation of the force and the hiker’s displacement at each moment.
(c) Using your answers to parts (a) and (b), discuss which, if either, of these forces can be associated with a potential-energy function. Support your conclusion with reasoning that refers to properties of the work done by each force over closed paths.