Question

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.

Answer 1

Step-by-step explanation:

It is given that,

Average power per unit mass generated by Lance,
`(P)/(m)=6.5\ W/kg`

`P=6.5* 75=487.5\ W`

(a) Distance to cover race,
`d = 160\ km =160* 10^3\ m`

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

If t is the time taken to cover the race.

`t=(d)/(v)`

`t=(160* 10^3\ m)/(11\ m/s)`

t = 14545.46 s

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

`P=(W)/(t)`

`W=P* t`

`W=487.5* 14545.46`

W = 7090911.75 J

(b) Since,
`1\ J=2.389* 10^(-4)\ calories`

So, in 7090911.75 J,
`W=7090911.75 * 2.389* 10^(-4)`

W = 1694.01 J

Hence, this is the required solution.