coefficient of friction

**jon_mro** · April 6th 2008, 03:16 AM

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

**bobak** · April 6th 2008, 04:03 AM

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 $\mu$

**jon_mro** · April 6th 2008, 04:55 AM

thank you for your reply is the answer 17.01

**earboth** · April 6th 2008, 05:28 AM

Originally Posted by jon_mro

thank you for your reply is the answer 17.01

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 $\mu$ :

$\mu = \frac{3600-450 \cdot 9.81 \cdot \frac12\ N}{450 \cdot 9.81 \cdot \frac12 \sqrt{3}\ N} \approx 0.3643$

**bobak** · April 6th 2008, 06:34 AM

also you should know that $\mu$ can only take values between 0-1. that should be written in your books somewhere.

**Mathstud28** · April 6th 2008, 08:20 AM

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

**bobak** · April 6th 2008, 08:32 AM

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.

**Mathstud28** · April 6th 2008, 08:35 AM

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

**topsquark** · April 6th 2008, 09:20 PM

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

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