# A little assistance with Friction mu k

• tducote
In summary, a skier with a mass of 62 kg skis down an icy slope with a length of 69 m at an angle of 32°. At the bottom, the path levels out and becomes horizontal, causing the skier to slow down and come to a stop in a distance of 160 m. The speed of the skier at the bottom of the slope is 26.7 m/s. In order to find the coefficient of kinetic friction between the skier and the horizontal surface, we can use Newton's 2nd law by considering the skier's acceleration and the only horizontal force acting on the skier. This results in a coefficient of kinetic friction of approximately 0.04.
tducote

## Homework Statement

A skier with a mass of 62 kg starts from rest and skis down an icy (frictionless) slope that has a length of 69 m at an angle of 32° with respect to the horizontal. At the bottom of the slope, the path levels out and becomes horizontal, the snow becomes less icy, and the skier begins to slow down, coming to rest in a distance of 160 m along the horizontal path.

a) What is the speed of the skier at the bottom of the slope?
m/s
i solved a) and got that it was 26.7 m/s for the speed

B is what i am having trouble with
b) What is the coefficient of kinetic friction between the skier and the horizontal surface?
µk =

## Homework Equations

fmax= mu k N i think

## The Attempt at a Solution

I tried many different ways...
26.7/607.6 = uk .04
uk mgcos(theta) = ma
uk 62(9.8cos32) = (5.19)(62) = .6 ... something

I am still confused about how to solve this any hints or techniques would greatly be appreciated

P.S. this is my first post please be kind :)

tducote said:
fmax= mu k N i think
Close enough: f_k = mu_k N (No need for max--you were thinking of static friction.)

Hint: The frictioned section of the path is horizontal.

What's the skier's acceleration?
What's the only horizontal force acting on the skier?
Apply Newton's 2nd law and solve for mu_k. (What's N?)

Dear student,

First of all, congratulations on solving part a) correctly! It shows that you have a good understanding of the concepts involved in this problem.

Now, for part b), we can use the equation you mentioned: fmax = µkN, where fmax is the maximum frictional force, µk is the coefficient of kinetic friction, and N is the normal force. We can rearrange this equation to solve for µk:

µk = fmax/N

We know that at the bottom of the slope, the only force acting on the skier is the frictional force, since the slope is now horizontal and there is no longer a component of the force of gravity acting in the direction of motion. Therefore, we can say that:

fmax = ma

where m is the mass of the skier and a is the acceleration (which is equal to the deceleration in this case). We can calculate the acceleration using the equations of motion:

v^2 = u^2 + 2as

where v is the final velocity (which we know from part a)), u is the initial velocity (which is 0 since the skier starts from rest), and s is the distance traveled (which we also know from the problem).

Plugging in the values, we get:

(26.7 m/s)^2 = 0 + 2a(160 m)

Solving for a, we get a = -0.223 m/s^2 (note the negative sign, indicating deceleration).

Now, we can plug this value for a into our equation for fmax:

fmax = ma = (62 kg)(-0.223 m/s^2) = -13.866 N

Since the normal force, N, is equal to the weight of the skier (mg), we can calculate it as:

N = (62 kg)(9.8 m/s^2) = 607.6 N

Finally, we can plug these values for fmax and N into our equation for µk:

µk = fmax/N = (-13.866 N)/(607.6 N) = -0.0228

It is important to note that the coefficient of friction is a dimensionless quantity and can never be negative. In this case, the negative sign indicates the direction of the force (in this case, opposite to the direction of motion). Therefore, we can say that the coefficient of kinetic friction

## What is friction?

Friction is a force that occurs when two surfaces rub against each other. It is caused by the irregularities on the surfaces and results in resistance to movement.

## What is the coefficient of friction?

The coefficient of friction, represented by the symbol μ (mu), is a dimensionless number that indicates the amount of friction between two surfaces. It is a measure of the force needed to move one surface over the other.

## What is the difference between static and kinetic friction?

Static friction is the force that prevents two stationary surfaces from moving relative to each other, while kinetic friction is the force that opposes the movement of two surfaces that are already in motion.

## How does the coefficient of friction affect the force of friction?

The higher the coefficient of friction, the greater the force of friction. This means that surfaces with a higher coefficient of friction will require more force to move them against each other.

## What factors affect the coefficient of friction?

The coefficient of friction can be affected by the type of surfaces in contact, the roughness of the surfaces, the amount of force applied, and the presence of any lubricants or other substances between the surfaces.

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