Question

A skier of mass 70 kg is pulled up a ski slope by a motor driven cable. How much work is required to pull him 60 m up a 30 °slope (assuming it's frictionless) and moves at a constant speed of 2 m/s.

Answer 1

To solve this problem we will apply the work theorem. Here we will start from the fact that this is the product between the Force applied and the distance traveled by the object. For the particular case of the inclined plane, the net work will be the one necessary to move the weight component, that is when  $mgsin\theta$ acts along the plane.

Then the work would be,

$W = (mgsin\theta)d$

Here d is the distance traveled by the object and $\theta$ is angle of inclined plane

$W = (70)(9.8)Sin 30(60)$

$W = 20.580J$

$W \approx 20.5kJ$

Therefore the work required is 20.5kJ approximately