Solving for Slope Angle from Kinetic Friction

[supraroy19]

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 don't 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 equation 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 can't figure out how to do it without those variables.

 

[JaredJames]

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.

 

[gneill]

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 don't 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 equation 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 can't 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

 

[ashishsinghal]

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

 

[rwisz]

I would approach this problem by first defining the variables and equations that are relevant to the situation. In this case, the skier's speed (4 m/s) and the coefficient of kinetic friction (0.2) are given. The angle of the slope, which we will call theta (θ), is what we are trying to solve for. We can also assume that the skier's mass (m) and the acceleration due to gravity (g) are constant.

To solve for the angle of the slope, we can use the equation for the net force acting on the skier, which is equal to the product of their mass and acceleration (F=ma). In this case, the net force is also equal to the force of friction (Ff), which can be calculated using the formula Ff=μmg, where μ is the coefficient of friction, m is the mass, and g is the acceleration due to gravity.

Since the skier is moving at a constant speed, we can also assume that the net force is equal to zero (since there is no acceleration). This means that the force of friction is equal and opposite to the force of gravity acting on the skier. We can represent this using vector diagrams, where the force of friction is pointing uphill and the force of gravity is pointing straight down.

Using trigonometry, we can see that the angle of the slope (θ) is equal to the inverse tangent of the coefficient of friction (μ). This is because the force of friction is equal to the force of gravity multiplied by the sine of the angle of the slope (Ff=mg*sinθ), and the force of gravity can be represented as mg*cosθ. So, by dividing the two equations, we get Ff/mg = sinθ/cosθ, which simplifies to μ=tanθ.

In summary, to solve for the angle of the slope, we can use the equation μ=tanθ, where μ is the coefficient of friction given in the problem. The velocity (4 m/s) does not factor into this equation because it is not directly related to the forces acting on the skier. The weight of the skier is also not needed because it cancels out when we set the net force equal to zero. The angle of the slope can be determined solely based on the coefficient of friction.