Calculus 2 A superman cyclist rode a bike uphill at 20 miles

Calculus 2

A superman cyclist rode a bike uphill at 20 miles/hour for two hours. To sustain this constant speed the cyclist was exerting 50 pounds.

(a) How much work has the cyclist done during the trip?

(b) How many power bars are needed to make up for the lost energy? Assume that one power bar has 300kcal and that a fit person\'s energy conversion efficiency is 25\\%. Google the the needed conversion formulas.

Solution

We know that for a constant force being F being applied to sustain a speed of v, the power being used is given as:

P = F x V

or P = 50 x 20 = 50 x 4.44822 x 20 x 1.60934 x (5/18) = 1988.527 W [Since 1 pound force =4.44822 N and 1 mile = 1.60934 Km]

Also, we know that for a power P being utilised for a time of t, the net work done is given as W = P x T

a.) or W = 1988.527 x 2 x 3600 = 14317.39675 kJoules

b.) Now each power bar gives 0.25 * 300 kCal = 75 kCal

Therefore the required number of bars would be: 14317.39675 / 75 x 4.184 = 45.626

Hence the cyclist will have to have 46 bars to replenish the energy.