Answer:
a) 261.4 W b) 1, 568.5 kJ = 374.7 Kcal
Explanation:
In order to find out the mechanical power spent by a top climber, we need to find first the energy used to climb.
This energy is supplied by the body, and must be equal to the change in gravitational potential energy, as follows:
U = m. g . h
In order to find out the height (vertically) climbed, we need to multiply the height of one step times the quantity of steps.
The horizontal displacements along any step don´t add to the total energy as the body does not work when moves horizontally.
So, h can be calculated as follows:
h = 0.18 m x 2,223 steps = 400.1 m
Replacing in (1), we have:
U = 80 kg. 9.8 m/s2 .400. 1 m = 313.7 kJ
As we have the energy and the time used to spend the energy, we can get the power, as follows:
P = U / t = 313. 7 KJ / 1200 sec = 261.4 W
b) If only 20% of the chemical energy produced by the body is converted to the mechanical energy used to climb, this means that the chemical energy produced must be larger, as follows:
E = U / 0.2 = 313.7 kJ / 0.2 = 1,568.5 kJ
As 1 Kcal =4,186 J, we have:
E(Kcal) = 1,568.5 kJ / 4,186 J = 374.7 Kcal
