# How do you find the angle of a slope if you are only given coefficient of friction

A skier is traveling at a constant speed of 4 m/s on a ski slope. The kinetic coefficient of frictionbetween her skis and the slope is 0.2. Find the angle of the slope.

attempt:

sin feda = f/w but i have no weight
f=mgsinfeda and N=mg cos feda
all of this ends up being mu=tan feda but dont understand where the Velocity in the problem factors in or if since its a constant force and the net sum of a constant moving anything is zero if it does not factor into the equasion at all. i have drawn a vector sum diagram with net sum =0. We worked out one of these in class but he gave us the wieght of the person and the angle. i cant figure out how to do it without those variables.

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## Answers and Replies

I will gladly assist you with the problem, but you must show your attempt at a solution before I can do so as per PF rules.

EDIT: Attempt added noted.

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gneill
Mentor

A skier is traveling at a constant speed of 4 m/s on a ski slope. The kinetic coefficient of frictionbetween her skis and the slope is 0.2. Find the angle of the slope.

attempt:

sin feda = f/w but i have no weight
f=mgsinfeda and N=mg cos feda
all of this ends up being mu=tan feda but dont understand where the Velocity in the problem factors in or if since its a constant force and the net sum of a constant moving anything is zero if it does not factor into the equasion at all. i have drawn a vector sum diagram with net sum =0. We worked out one of these in class but he gave us the wieght of the person and the angle. i cant figure out how to do it without those variables.

Generally you will find with these sorts of problems that information that is not given (such as weight or mass) will eventually cancel out in the equations involved. So unless you're "addicted" to plugging in numbers as soon as possible for every case, there shouldn't be a problem.

In this case the skier is said to be traveling at a constant speed downhill. That implies no acceleration, and hence no force imbalance. So you need to find expressions for the forces involved. If you assume that the skier has a mass "m", what are expressions for the downhill force due to gravity and the frictional force?

Oh, and here's a ---> θ <--- for cutting and pasting i posted the solution but knowing the rules had to delete it:
giving you a hint:
if velocity is constant; net force = 0
just equate all forces in it