# Finding the Coefficient of Friction

• xcsyl
In summary, an ice skater moving at 10.0 m/s comes to a halt in 100 m on a smooth ice surface. The coefficient of friction between the ice and the skates is 0.051, which is equal to the frictional force divided by the normal force. Using equations for motion and force, it can be determined that the acceleration of the skater is -0.5 m/s^2 and the normal force is equal to the skater's weight, mg. The coefficient of friction for "steel-on-ice" is typically around 0.05.
xcsyl

## Homework Statement

An ice skater moving at 10.0 m/s coasts to a halt in 1.0 x 10^2 m on a smooth ice surface. What is the coefficient of friction between the ice and the skates?

## Homework Equations

coefficeint of friction = kinetic friction/Normal force
(µk = Fk/Fn)
Σ Fy = may
Σ Fx = max

## The Attempt at a Solution

I've tried many different approaches, using motion equations, and somehow end up confused in all of them. Maybe I picked the wrong equations and this problem is simpler than I'm making, but I'm not sure. I'm having problems with incorporating motion equations with force equations. Here's one of my attempts. Thanks! (I know the answer is 0.051, but I can't get to that number)

My attempt:
⌂x = 100 m
Vi= 10 m/s

Σ Fy = Fn - mg = may

⌂x = .5(Vf + Vi)⌂t
100 = .5(0+10)⌂t
⌂t= 20 s

Vf^2=Vf^2 + 2a⌂x
0=100 + 2a(100)
-100 = 200a
a=-.5

[EDIT] I'm pretty sure I found my mistake! I still would like to see this worked out, but the answer is .051 not .51, sorry I'll change that.

Last edited:
You know the acceleration, so what is the magnitude of the resultant force on the skater?
This resultant force is equal to the friction. The friction is proportional to Fn. Fn=mg.

ehild

Ahhh I wrote down the answer wrong once again.. sorry. It's .051 not .51
That's what I can't quite figure out past getting acceleration. Again sorry! I'm getting my numbers jumbled

Ooh I also found in my book what some objects on surfaces have as coefficients of friction and "steel-on-ice" is .05. I still want to be able to work this out, and thanks ehild for that. I'm using Fn=mg as well, thanks!

Last edited:

## What is the coefficient of friction?

The coefficient of friction is a measure of the amount of resistance between two surfaces in contact, which determines the force needed to move one surface over the other. It is represented by the Greek letter mu (μ) and is a unitless value.

## Why is it important to find the coefficient of friction?

The coefficient of friction is important because it helps us understand the behavior of objects in motion and the forces acting on them. It is also used in engineering and design to determine the best materials and surface finishes for different applications.

## How is the coefficient of friction determined?

The coefficient of friction can be determined experimentally by measuring the force required to move an object of known weight over a surface. The ratio of these two values gives the coefficient of friction. It can also be calculated using mathematical equations based on the properties of the surfaces in contact.

## What factors affect the coefficient of friction?

The coefficient of friction can be influenced by several factors such as the type of materials in contact, the roughness or smoothness of the surfaces, the amount of force applied, and the presence of any lubricants. It can also vary with temperature and humidity.

## How does the coefficient of friction impact everyday life?

The coefficient of friction plays a significant role in our daily lives, influencing activities such as walking, driving, and even cooking. It helps us understand the safety of different surfaces and the effectiveness of various products like tires, shoes, and non-stick cookware. It also affects the efficiency and performance of machines and equipment used in industries such as transportation and manufacturing.

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