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?
2007-02-02 14:44:23 · 5 answers · asked by venom90011@sbcglobal.net 1 in Science & Mathematics ➔ Physics
the magnitude us 13.952786. i'm not sure if that's right, but i'n pretty sure.
2007-02-02 14:50:56 · answer #1 · answered by geralyn p 1 · 0⤊ 0⤋
First find the vertical distance. The angle of the grade is arctan(.079) = 4.517 degrees. So the vertical distance is
13,800 * sin(4.517) = 1086.8 meters.
The work (or energy) involved in raising any mass against gravity is simply the potential energy due to gravity:
PE = g m h
where g is gravitational acceraltion (9.8 m/sec^2), m is mass in kg, and h is height in meters. So in the present case
PE = 9.8 * 83 * 1086.8
PE = 884,014 joules
2007-02-02 23:18:37 · answer #2 · answered by Keith P 7 · 0⤊ 0⤋
To determine the work done we need to know the vertical rise for the 13.8 km climb.
The angle of inclination is the tangent inverse of the grade: 0.079.
Tan INV(0.079) = ~4.52 degrees
The vertical rise is
13.8 km * sin(4.52) = 1.086 km
The amount of work done against the force of gravity is then
83 kg * 9.8 m/s^2 * 1.086 km = 8840.14 kilo Joules
2007-02-02 23:59:06 · answer #3 · answered by sandcrafter 1 · 0⤊ 0⤋
sin(inclination)*distance*mass
2007-02-02 22:57:32 · answer #4 · answered by lightpulse 4 · 0⤊ 0⤋
I think it is 13.953
2007-02-02 22:59:23 · answer #5 · answered by Mike C 3 · 0⤊ 0⤋