Help me check the coefficient in this problem, physics?

Question

A toboggan slides down a hill and has a constant velocity. The angle of the hill is 8.00o with respect to the horizontal. What is the coefficient of kinetic friction between the surface of the hill and the toboggan?

my ans: 0.141

can you show your solution?

im not sure how to find the Fn and Ff

Answer 1

Let:

u be the coefficient of kinetic friction,

m be the mass of the toboggan,

g be the acceleration due to gravity.

Parallel to the slope, as there is no acceleration:

mg sin(8) - Ff = 0

Ff = mg sin(8) ...(1)

Perpendicular to the slope, as there is no motion:

mg cos(8) = Fn ...(2)

Ff / Fn = u ...(3)

Dividing (1) by (2) and substituting in (3):

[ mg sin(8) ] / [ mg tan(8) ] = u

u = tan(8) = 0.141.

You cannot find the values of Ff and Fn unless you know the mass of the toboggan, but these values are not asked for.