What is the kinetic friction coefficient?

[Kailee]

Homework Statement

A skier is sliding down a 20^o slope at constant speed, what is the kinetic friction coefficient?

Homework Equations

E = 1/2 mv²
W = Fd
F = ma
F = μN = μmg

The Attempt at a Solution

Attempted to use ma = μmgsin20, which crosses out the masses since mass was not given, but the skier is going at a constant speed so I'm assuming acceleration would be zero. Though I'm not sure how to continue the question or if I'm on the right track. Thanks in advance!

 

[brainpushups]

Have you tried drawing a force diagram? If not, start here. You'll notice that your expression for the force of friction is incorrect (the μmg part), and that you have left out a force along the slope (the component of a force to be more specific)

You are correct that the acceleration would be zero.

 

[Kailee]

Ah, figured out what I was doing wrong, thank you! :)

 

[siddharth23]

You're right, the acceleration is zero. But you are missing one force. Why don't draw an FBD of the skier on the incline.

 

[HalfLostAndSearching]

The kinetic friction coefficient is a measure of the amount of friction between two surfaces in motion. It is denoted by the symbol μ (mu) and is a unitless quantity. It represents the ratio of the force of kinetic friction (F) to the normal force (N) between the two surfaces.

In this scenario, the skier is sliding down a slope at constant speed, which means that the net force acting on the skier is zero. This includes the force of gravity pulling the skier down the slope and the force of kinetic friction pushing against the skier's motion. Therefore, we can set up the following equation:

0 = F - mg sin 20

Where F is the force of kinetic friction, m is the mass of the skier, and g is the acceleration due to gravity. We can rearrange this equation to solve for the kinetic friction coefficient:

F = μN = μmg
μ = F/(mg) = (0)/(mg sin 20) = 0

This means that the kinetic friction coefficient in this scenario is zero, indicating that there is no friction between the skier and the slope. This could be due to the slope being very smooth or the skier using wax on their skis to reduce friction.