Question

Lance Armstrong bikes at a constant speed up the Alpe d'Huez, a famous mountain pass. Assume his teammates do such a good job riding ahead of him that he can draft behind them and encounter no air resistance. This climb is described as "beyond classification" in terms of its difficulty. The climb is 13.8 km long at a 7.9% average grade (the grade, as a decimal, is the tangent of the angle of inclination). Assume that the combined mass of Lance and his bicycle is 83 kilograms. What is the magnitude of the work he does against the force of gravity?

Answer 1

Answer:

$W=8.84*10^5J$

Explanation:

We should calculate the angle of inclination. We know that the grade, as a decimal, is the tangent of the angle of inclination. So, we have:

$\frac{7.9\%}{100}=0.079\\0.079=tan\theta\\\theta=arctan(0.079)\\\theta=4.52^\circ$

The vertical distance traveled by Lance is given by:

$y=dsin\theta\\y=(13.8km)sin(4.52^\circ)\\y=1.087km*\frac{1000m}{1km}=1087m$

The work done to raise a body to a certain height is equal to the amount of gravitational potential energy that the body stores when it reaches that height:

$W=mgy\\W=83kg(9.8\frac{m}{s^2})(1087m)\\\\W=8.84*10^5J$