Question

An elite Tour de France cyclist can maintain an output power of 450 W during a sustained climb. At this output power, how long would it take an 88 kg cyclist (including the mass of his bike) to climb the famed 1100-m-high Alpe d'Huez mountain stage?

Answer 1

Answer:

T = 35' 08"

Explanation:

• By definition, the power is the rate of change of energy, with respect to time:

       $P = \frac{\Delta E}{\Delta t} (1)$

• ΔE, in this case, must be equal to the change in the gravitational potential energy during the climb (neglecting friction), as follows:

       $\Delta E = m*g*h = 88 kg*9.8m/s2*1100 m = 948640 J (2)$

• From (1) and (2), being P= 450 W, we can solve for Δt, as follows:

       $\Delta t = \frac{\Delta E}{P} = \frac{948640J}{450W} = 2108 sec. (3)$

• Converting seconds to minutes, we get:
• Δt = 35' 08"