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Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by Lance Armstrong (m = 75.0 kg) is 6.50 W per kilogram of his body mass.
(a) How much work does he do during a 160-km race in which his average speed is 11.0 m/s?

(b) Often, the work done is expressed in nutritional Calories rather than in joules. Express the work done in part (a) in terms of nutritional Calories, noting that 1 joule = 2.389x10^-4 nutritional Calories.

Respuesta :

Explanation:

It is given that,

Average power per unit mass generated by Lance, [tex]\dfrac{P}{m}=6.5\ W/kg[/tex]

[tex]P=6.5\times 75=487.5\ W[/tex]

(a) Distance to cover race, [tex]d = 160\ km =160\times 10^3\ m[/tex]

Average speed of the person, v = 11 m/s

If t is the time taken to cover the race.

[tex]t=\dfrac{d}{v}[/tex]

[tex]t=\dfrac{160\times 10^3\ m}{11\ m/s}[/tex]

t = 14545.46 s

Let W is the work done. The relation between the work done and the power is given by :

[tex]P=\dfrac{W}{t}[/tex]

[tex]W=P\times t[/tex]

[tex]W=487.5\times 14545.46 [/tex]

W = 7090911.75 J

(b) Since, [tex]1\ J=2.389\times 10^{-4}\ calories[/tex]

So, in 7090911.75 J, [tex]W=7090911.75 \times 2.389\times 10^{-4}[/tex]

W = 1694.01 J

Hence, this is the required solution.

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