Question

The boy pulls a sledge weighing 5 kg on the snow with the help of a rope that builds an angle of 60 ° with the horizontal direction. The force with which the boy pulls the rope is 10 N, and the sled moves at a constant speed. Determine the coefficient of friction between the sled and the snow surface.

Answer 1

The force of friction is

$$f=\mu N.$$

The normal force N can be found from the following condition:

$$N-mg+F\sin60°=0,\\\space\\ \mu=\frac fN=\frac{f}{mg-F\sin60°}.$$

Since the sled moves at a constant velocity, we have the following equilibrium of the pulling force and the friction:

$$f-F\cos60°=0,\\ f=F\cos60°.$$

Therefore:

$$\mu=\frac{F\cos60°}{mg-F\sin60°}=0.124.$$