Question

(II) A skier moves down a 12° slope at constant speed. What can you say about the coefficient of friction, Assume the speed is low enough that air resistance can be ignored.

Answer 1

Use Newton’s second law of motion and the equation for frictional force to calculate the coefficient of kinetic friction.

According to Newton’s second law, the net force acting on a box is equal to the product of mass of the box and its acceleration. Mathematically it is given as,

Here, is the mass of the box and is the acceleration of the box.

The figure represents the free body diagram of the skier moving down the slope and the forces acting on him.

$C:\Users\subhani\10..12.jpg$

Since the skier is moving down, the friction force acting on him is,

Here, is the frictional force acting on the box, is the coefficient of kinetic friction, and is the normal force acting on the box.

Apply Newton’s second law alongdirection.

Substituteforin equation.

Apply Newton’s second law alongdirection.

Since the skier is moving with a constant speed so the acceleration of the skier along x and y-directions will be zero.

Now equate the equationand.

Substitutefor and solve for.

Thus, the coefficient of kinetic friction is. This value of coefficient of kinetic friction is very small.