Question

Lance Armstrong is accelerating up one of the hills on his bike in The Tour de France. The
combined mass is 80.0 kg. The hill is 650 m long and the total elevation change of the
hill is 25 m. His speed at the bottom of the hill is 2.0 m/s. Lance reaches the top of the
hill in 150 seconds and is traveling at 7.5 m/s. If force of friction on the bike
wheels is 35 N, find the average human power

Answer 1

Answer on Question #71211-Physics-Other

Lance Armstrong is accelerating up one of the hills on his bike in The Tour de France. The combined mass is 80.0 kg. The hill is 650 m long and the total elevation change of the hill is 25 m. His speed at the bottom of the hill is 2.0 m/s. Lance reaches the top of the hill in 150 seconds and is traveling at 7.5 m/s. If force of friction on the bike wheels is 35 N, find the average human power

Solution

Total work is

$$W = \Delta \mathrm{KE} + \Delta \mathrm{PE} + W_{fr}$$ $$\Delta \mathrm{KE} = \frac{1}{2} m \left(v_{f}^{2} - v_{l}^{2}\right) = \frac{1}{2} 80 \left(7.5^{2} - 2^{2}\right) = 2090 \, J$$ $$\Delta PE = 80 \cdot 9.8 \cdot 25 = 19600 \, J$$

Work done by the friction force is

$$W_{fr} = F_{fr} l = 35 \cdot 650 = 22750 \, J$$

Total work is

$$W = 2090 + 19600 + 22750 = 44440 \, J$$

Power is

$$P = \frac{44440}{150} = 300 \, W.$$

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