Question

Sprinting up a short flight of stairs is often used as a simple test to compare power output among different athletes. Subject 1, a football player with a body mass of 130 kg, sprints up a flight of stairs and raises his body mass 4.4 m vertically in a time of 3.4 s. Subject 2, a cyclist with a body mass of 75 kg, sprints up the same flight of stairs in 2.8 s. Determine the mechanical work and power for both of these athletes. Which athlete is more powerful in an absolute sense (W)? What if power is expressed relative to body mass (W/kg)? Assuming that the body is 25% efficient, determine the amount of metabolic energy spent during this stair sprint for both athletes (total Kcals, not Kcal/hour; Hint: 1 J = 0.000239 Kcals).

Answer 1

Hey there!:

subject 1

Mechanical work =mgh

= 130 *9.8 *4.4

= 5605.6 J

Mechanical power =Work/time

= 5605.6 / 3.4

= 1648.706 W

Subject 2

Mechanical work =mgh

= 75 * 9.8 * 4.4

= 3234 J

Mechanical power =Work/time

= 3234/2.8

= 1155 W

Athlete 1 is more powerful in absolute sense

relative to mass

athlete 1 power =12.68 W/kg

athlete 2 power =15.4 W/kg

thus athlete 2 is more power in relative to mass power .

metabolic energy spent by athlete 1 :

= (5605.6 / 0.25)*0.000239 kCal

= 5.359 kCal

metabolic energy spent by athlete 2=(3234/0.25)*0.000239 kCal

= 3.092 kCal

Hope this helps!