Question

A bicyclist maintains a constant speed of 4.00 m/s up a hill that is inclined at 10.0∘ with the horizontal. Calculate the work done by the person and the work done by gravity if the bicycle moves a distance of 18.0 m up the hill. The combined mass of the rider and the bike is 82.0 kg. 1) Calculate the work done by gravity. (Express your answer to three significant figures.)

Answer 1

the work done by the person
`W_p=2.52*10^3J`

the work done by gravuty
`W_g=-2.52*10^3J`

Step-by-step explanation:

Because the velocity is constant the cyclist has to excert a force equal to the component of the weight.

`F_c-F_w=0`

`F_w=m*g*cos(\theta)\\F_w=82.0*9.81*sin(10^o)\\F_w=140N`

The work done by the person is given by:

`W_p=F_c*d\\W_p=140N*18.0\\W_p=2.52*10^3J`

and the work done by the gravity:

`W_g=F_g*d\\W_g=-82.0*9.81*sin(10)*18.0\\\\W_g=-2.52*10^3J`