A cyclist and bicycle together have a combined mass of
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power
Problem
A cyclist and bicycle together have a combined mass of 75kg. During a mountain climb the cyclist maintains a steady mechanical power output of 250W directed entirely toward gaining gravitational potential energy. The route gains a total elevation of 1200m over a horizontal distance of 15km. Ignore energy losses due to air resistance and rolling friction.
(a) Calculate the minimum time required for the cyclist to complete the climb if all of the cyclist’s power is used to increase gravitational potential energy.
(b) Determine the total mechanical energy expended in completing the climb, in joules.
(c) A nutrition label states that 1 dietary Calorie (1Cal) equals 4.186kJ. Estimate how many Calories of food energy the cyclist must convert to mechanical work to perform the climb, assuming the cyclist’s body is 25% efficient in converting chemical energy into mechanical power.
(d) Professional cyclists often complete such climbs in less time than calculated in part (a). Identify two physical factors neglected in this idealized model that could account for the discrepancy, and briefly explain the qualitative effect each factor would have on the required power.