Average coefficient of friction

[Bones]

Homework Statement

A skier traveling 11 m/s reaches the foot of a steady upward 22° incline and glides 13 m up along this slope before coming to rest. What was the average coefficient of friction?

Homework Equations

The Attempt at a Solution

Can someone help me get started by helping me with the equation and figuring out how mass cancels out?

 

[Bones]

I figured this one out ;)

 

[baba89]

As a scientist, it is important to approach this problem using the appropriate equations and concepts. In this case, we can use the equation for the work-energy principle, which states that the work done by a force is equal to the change in kinetic energy. In this case, the only force acting on the skier is the force of friction, which is given by the equation Ff = μmg, where μ is the coefficient of friction, m is the mass of the skier, and g is the acceleration due to gravity.

Since the skier starts with a velocity of 11 m/s and comes to rest after traveling 13 m up the incline, the work done by the force of friction is equal to the change in kinetic energy, which can be written as:

W = ΔKE = 1/2mvf^2 - 1/2mvi^2

Where vf is the final velocity (0 m/s) and vi is the initial velocity (11 m/s).

Substituting in the values and solving for the coefficient of friction, we get:

μ = (2W)/(mgd)

Where W is the work done by friction, m is the mass of the skier, g is the acceleration due to gravity, and d is the distance traveled up the incline (13 m).

To find the work done by friction, we can use the equation W = Ff*d, where Ff is the force of friction and d is the distance traveled. Substituting in the values, we get:

W = μmgd

Plugging this back into the original equation, we get:

μ = (2μmgd)/(mgd) = 2

Therefore, the average coefficient of friction for this scenario is 2. This means that the force of friction acting on the skier was twice the weight of the skier. It is important to note that this value may seem high, but it is likely due to additional factors such as the texture of the slope and any external forces acting on the skier.