Question

A 52 kg skier stars from rest and glides down a 45° incline for a distance of 30 m. What are the components of the weight?

Answer 1

The perpendicular component is `F_|_=F_gcostheta=360.3N`

The parallel component is `F_(||)= F_gsintheta=360.3 N`

Explanation:

If a body is placed on an incline that makes an angle `theta` with the horizontal, the components of the force of gravity are drawn such that one points along the incline, and the other is perpendicular to it.

The angle `theta` between `F_(grav)` and `F_|_` in the right diagram above will necessarily be the same as the angle made by the ramp.

The components are

`F= F_(grav) cos theta=52(9.8)(0.707) = 360.3N`

(can't get the "perpendicular" symbol to work here for some reason!)

`F_(||)=F_(grav) sin theta52(9.8)(0.707) = 360.3N`

(The two values are equal because of the 45° angle. This is generally not the case.)