A top cyclist in the Tour de France is competing in an individual time trial, in

Question

A top cyclist in the Tour de France is competing in an individual time trial, in which the rider races a relatively short distance alone, trying to complete the course as quickly as possible. The relevant data for the cyclist is as follows: distance traveled is 27.0 km time elapsed is 43.0 minutes; average power output is 385 watts. (a) Calculate the cyclist's total energy output, in kilojoules, during the time trial kJ (b) There are 4184 joules in 1 kilocalorie. How many kilocalories are expended by this cyclist during the time trial? For comparison, the average person takes in (and expends) about 2500 kilocalories in food energy every 24 hours. kCal (c) Let's say the you were able to output the same total energy as the cydist, but you did this while climbing stairs. If your mass is 50.0 kg, and we take g 9.8 m/s2, how high up would you go? (Assume all your energy output goes into raising your gravitational potential energy.) For comparison, the Empire State building is about 450 m from the ground to the tip of its antenna

Explanation / Answer

a)

P= E/t

E= P*t = 385*(43*60) = 9.93*10^5 J

b)

E = 993300 J = (993300/4184) kilocalories = 237.40 kilocalories

c)

PE = mgh

h= PE/mg

h=993300/(50*9.8)

h= 2027.14 m

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