# Given: A bike rider traveled on his bike uphill at 20 miles per hour for two hours. To sustain this constant speed the cyclist was exerting 50 lbs. Unknown:  How many energy bars are needed to make up for the lost energy? Assume that one energy bar has 300kcal and that a fit person's energy conversion efficiency is 25%. You may use the web to look up the needed conversion formulas.

The force the cyclist exerts on the bike is

`F =50 lbs =50*0.4536 kg =22.68 kg =22.68*9.81 =222.491 N`

The speed of the cyclist is

`v =20 (mph) =20*1.609 ((km)/h) =32.18 ((km)/h) =32180/3600 (m/s) =8.939 m/s`

The power generated by the cyclist is

`P =F*v =222.491*8.939 = 1988.82 W`

The work done by cyclist for two hours is

`W = P*t =1988.82*2*3600 =1.432*10^7 J`

The energy intake per one bar is (25% from the total energy of a bar) (1 cal =4.18 J)

`E =0.25*300*10^3*4.18 =3.135*10^5 J`

Total number of energy bars necessary to be eaten is

`n = W/E =(1.432*10^7)/(3.135*10^5) =45.678 =46 "bars"`

The total number of energy bars needed to make up for the loss of energy is 46.

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