A hiker of mass starts at the base of a canyon and follows a piecewise path described…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power
Problem
A hiker of mass 70kg starts at the base of a canyon and follows a piecewise path described below:
1. Ascends vertically to the rim, a height of 60m above the starting point.
2. Descends into an adjacent valley 35m below the rim.
3. Climbs a lookout tower that stands 25m above the valley floor.
Assume the local gravitational field is uniform with magnitude g=9.8m⋅s−2. Neglect any horizontal motion and energy losses.
(a) Compute the change in gravitational potential energy of the hiker–Earth system for each segment separately, taking the canyon base as zero potential energy.
(b) Determine the net change in gravitational potential energy after the hiker reaches the top of the tower. State whether the final value is positive, negative, or zero relative to the starting point.
(c) Calculate the total mechanical work that the hiker’s muscles must perform to complete the entire trip, assuming the upward segments occur at constant speed and no regenerative work is obtained on the descent.
(d) Suppose the hiker had instead climbed directly from the canyon base to the top of the tower along a single vertical ladder. Using energy considerations, explain whether the mechanical work required would be different from the amount found in part (c).