# Coefficient of Friction problem

• demode
In summary, the coefficient of friction between a sled and a plane inclined at 30 degrees from the horizontal is mg sin(30) - μk*mgcos(30), where μk is the net force acting on the sled.
demode
The question states: "What is the coefficient of friction between a sled and a plane inclined at 30 degrees from the horizontal if the sled just slides without accelerating when given an initial push?"

I have drawn a free-body diagram and labeled all of the forces (I think i labeled all of them) but now I don't know what to do.. What equations will I need to write and what numbers will I need to use? If somebody could guide me through this it would be most appreciated..

Welcome to the forums,

Could you describe your FBD, what forces do you have acting in which directions?

There is one error there, would the weight really be acting in that direction?

Whoops, shouldn't it be going from the sled STRAIGHT down, perpendicular to the bottom of the triangle?

demode said:
Whoops, shouldn't it be going from the sled STRAIGHT down, perpendicular to the bottom of the triangle?
Indeed it should.

With that being said, I am going to need to write my equations.. I believe that frictional force can be modeled with the equation (Ff = μ Fn) and Fn in this context is equal to mgcos30. Also, mgsin30 minus the frictional force would be equal to ma. However, if we don't know M how can we solve for the coefficient of friction in the first equation?

I assume you with M means the mass of the sled.

Why don't you set up Newton's 2.law and see what can be done with that pernicious M?

I still don't understand what to substitute into Newton's 2.Law; Acceleration must be zero if the sled slides without accelerating with an initial push, and we don't know the value for m, as well as the value for the net force.. By playing around with the forces I labeled, I got the equation (mgsin30 - μk*mgcos30) = ma) but this may not be correct.

Ahhh, I can't seem to understand this =(

"Also, mgsin30 minus the frictional force would be equal to ma."

Correct!
Hence, with a=0, do you agree that we have:
$$mg\sin(30)=F_{fric}$$
where $F_{fric}$ is the frictional force?

I got the equation (mgsin30 - μk*mgcos30) = ma) but this may not be correct.
This IS correct.

So, what does that equation say when you know that a=0?

It will say after simplifying:

4.9m - μk * 8.48m = 0

To set in numbers is NOT simplification!
Do as follows:
$$mg\sin(30)=\mu{m}g\cos(30)$$
Now, divide with $mg\cos(30)$:
$$\frac{mg\sin(30)}{mg\cos(30)}=\frac{\mu{mg}\cos(30)}{mg\cos(30)}$$

Now, what factors cancels in each of the fractions?

ahh i got it now.. Thanks so much for your help everyone!

## What is the coefficient of friction?

The coefficient of friction is a measure of the amount of resistance present between two surfaces in contact with each other. It is a dimensionless value that is calculated by dividing the force required to move an object over a surface by the weight of the object.

## What factors affect the coefficient of friction?

The coefficient of friction can be influenced by several factors such as the nature of the materials in contact, the roughness of the surfaces, the temperature, and the presence of any lubricants or contaminants.

## How is the coefficient of friction measured?

The coefficient of friction can be measured using various methods such as the inclined plane test, the drag test, and the block-on-block test. These tests involve applying a known force to an object and measuring the amount of resistance it experiences while sliding over a surface.

## Why is the coefficient of friction important?

The coefficient of friction is important in many practical applications as it helps determine the amount of force needed to move an object over a surface, the amount of wear and tear on surfaces in contact, and the efficiency of machines and equipment.

## How can the coefficient of friction be reduced?

The coefficient of friction can be reduced by using lubricants to create a slippery layer between surfaces, by polishing or smoothing the surfaces to reduce their roughness, and by using materials with lower coefficients of friction.

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