# coefficient of friction

• Apr 6th 2008, 03:16 AM
jon_mro
coefficient of friction
can anybody show me how to work out :
a mass of 450kg on a smooth concerete floor , a force of 3.6kn is required to move it up a slope of 30 degrees determine the coefficient of friction between the floor and mass .

many thanks
• Apr 6th 2008, 04:03 AM
bobak
so a force of [LaTeX ERROR: Convert failed] is required to move it up this hill at a constant velocity.

so all the forces must be balanced.

Make sure you understand how the friction force is directed. It is down the plane because friction opposed the direction of motion (which is up the plane in this case).
So the forces going down the plane are the masses weight and the friction force.

so we have [LaTeX ERROR: Convert failed]

use exact values for sine and cosine and solve for $\mu$
• Apr 6th 2008, 04:55 AM
jon_mro
coefficient of friction
• Apr 6th 2008, 05:28 AM
earboth
Quote:

Originally Posted by jon_mro

How did you get this answer?

Take bobaks's equation, plug in all known values and solve for $\mu$:

$450\ kg \cdot 9.81\ \frac{m}{s^2} \cdot \underbrace{\sin(30^\circ)}_{= \frac12} + \mu \cdot 450\ kg \cdot 9.81\ \frac{m}{s^2} \cdot \underbrace{\cos(30^\circ)}_{= \frac12 \sqrt{3}} = 3600\ N$

Solve for $\mu$:

$\mu = \frac{3600-450 \cdot 9.81 \cdot \frac12\ N}{450 \cdot 9.81 \cdot \frac12 \sqrt{3}\ N} \approx 0.3643$
• Apr 6th 2008, 06:34 AM
bobak
also you should know that $\mu$ can only take values between 0-1. that should be written in your books somewhere.
• Apr 6th 2008, 08:20 AM
Mathstud28
Thats not true is it
I thought that $\mu$ could be greater than one...such as soft rubber on soft rubber?
• Apr 6th 2008, 08:32 AM
bobak
Quote:

Originally Posted by Mathstud28
I thought that $\mu$ could be greater than one...such as soft rubber on soft rubber?

I don't do advance mechanics but in my books (all per university), it says its limited between 0-1

I looked a some tables online and all the values seem to be within that range, but I haven't studied much on this topic.
• Apr 6th 2008, 08:35 AM
Mathstud28
Haha
Don't let what I say hold too much sway...I am only seventeen...and in honors physics...Math my is my forte...Physics...Is my nap time =D
• Apr 6th 2008, 09:20 PM
topsquark
Quote:

Originally Posted by Mathstud28
I thought that $\mu$ could be greater than one...such as soft rubber on soft rubber?

You are correct. $\mu$ can be as large as we want. That is not to say that it is likely to be greater than 1. In most (ordinary) circumstances it won't be.

So does there seem to be an upper limit on $\mu$? Soft rubber on soft rubber does not give a valid $\mu$ (as I understand the concept here) because as the rubber "slides" it also deforms. Breakage of the materials, deformation, wearing, etc. while sliding means that we can't measure a $\mu$ for that pair of materials. And, of course, if it won't slide at all that doesn't mean that $\mu \to \infty$, it means that we can't measure $\mu$ for that circumstance.

-Dan