A fitness study investigates the power output of a runner who sprints up a stadium…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power
Problem
A fitness study investigates the power output of a runner who sprints up a stadium staircase. The runner (mass = 68 kg) starts from rest at the bottom of the stairs and reaches the top, 26 m above the starting level, in 7.4 s.
While ascending, the runner also does work against a nearly constant 130 N resistive force due to air drag and internal friction in the joints.
(a) Calculate the increase in the runner’s gravitational potential energy during the ascent.
(b) Determine the total mechanical work the runner performs, taking into account both the elevation gain and the resistive force.
(c) Compute the runner’s average mechanical power output during the ascent.
(d) The metabolic efficiency of converting chemical energy into mechanical work for an athlete is approximately 25 %. Estimate the average rate at which the runner’s body converts chemical energy (metabolic power) during the sprint.
(e) Discuss one physiological or practical implication of the metabolic power calculated in part (d) for athletic training or performance.