Question

A bicyclist maintains a constant speed of 4.00 m/s up a hill that is inclined at 10.0 degrees with the horizontal. Calculate the work done by the person and the work done by gravity if the bicycle moves a distance of 19.0 m up the hill. The combined mass of the rider and the bike is 88.0 kg.

1) Calculate the work done by gravity.

2) Calculate the work done by the person.

Answer 1

constant speed V = 4.00 m/s

angle of inclination $\theta=10.0^{\circ}$

distance moved L = 19.0 m

mass m = 88.0 kg

since speed is constant, net work done by all forces is zero.$W_p+W_g=0$

1) work done by gravity = $W_g=-mgL\sin\theta=-88.0\times9.81\times19.0\times\sin{10.0^{\circ}}=-2848\,J$

2) work done by person = $W_p=-W_g=+mgL\sin\theta=88.0\times9.81\times19.0\times\sin{10.0^{\circ}}=2848\,J$