Coefficient of friction on a 30-degree incline

[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..

 

[Hootenanny]

Welcome to the forums,

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

 

[demode]

I whipped up a little diagram of what I thought the forces were

http://img415.imageshack.us/img415/6636/untitled1ov5.th.jpg

 

[Hootenanny]

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

 

[demode]

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

 

[Hootenanny]

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

Indeed it should.

 

[demode]

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?

 

[arildno]

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?

 

[demode]

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 =(

 

[arildno]

"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?

 

[arildno]

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?

 

[demode]

It will say after simplifying:

4.9m - μk * 8.48m = 0

 

[arildno]

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?

 

[demode]

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