# Rough Inclined Plane - Find Coefficient of friction

1. Feb 21, 2013

1. The problem statement, all variables and given/known data
a block of mass 2kg is in at rest on a rough plane inclined at 30°, it is in limiting equilibrium with with a force of 20N applied horizontally (to the ground).

Find the coefficient of static friction between the block and the plane.

3. The attempt at a solution
$R=mgcos30+20sin30\\ .\\ mgsin30-μR=20cos30\\ mgsin30-μmgcos30+μ20sin30=20cos30\\ 9.8-16.97μ+10μ=17.32\\ 9.8-26.97μ=17.32\\ -26.97μ=7.52\\ μ=-0.28\\$
Now I now my answer cannot be minus something as 0<μ<1, however, I am unsure as to whether it is my understanding of the question or the algebra I have got wrong. Im sure its a silly mistake, it usually is with me but any help or advice is greatly appreciated.

2. Feb 21, 2013

### Staff: Mentor

When you substituted the two terms of R, only one of them got the minus sign.

3. Feb 21, 2013

### Staff: Mentor

It looks like that was just a typo on your part and that your calculation did carry the minus sign throughout.

But you made an assumption about the direction of the friction force that may not be justified. Try interpreting the problem like so: If that 20 N force were any greater, the block would start to slide up the incline.

4. Feb 21, 2013