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 178-km race in which his average speed is 11.5 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 = 2.389 x 10^-4nutritional Calories.

Answer 1

(a) How much work does he do during a 178-km race in which his average speed is 11.5 m/s?

Work done be Lance Armstrong is given by:

$W=P*time......................(1)$

Now given that

Pkg = 6.5W/kg

$\Rightarrow P=6.5*75$

P= 487.511

Time to cover 178km(=178000m) race at the speed of 11.5m/s is given by

$\Rightarrow t=\frac{178000}{11.5}$

$\Rightarrow t=15478.261 sec$

for mass = 75 kg power is given by

Now Using Equation 1 to get the work done

$\Rightarrow W=P*time$

$\Rightarrow W=487.5*15478.261$

$\Rightarrow W=7545652.238J$

$\Rightarrow W=7545.65kJ$

(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 = 2.389 x 10^-4nutritional Calories.

SInce

1 joule = 2.389 x 10^-4nutritional calories

$\Rightarrow W=7545652.238*2.389 x 10^{-4}$

$\Rightarrow W=1802.656 calories$?