Find Coefficient of Friction only given angle at which object slides on ramp.

[avsj]

Homework Statement

A block of wood is sitting on an inclined plane. One end of the plane is rised until the wood block slides down. The wood block slides down when the plane has an angle of 30 degrees to the horizontal. What is the coefficient of friction?

Homework Equations

uFn=Ff

Fnet = Fd + Ff

In this case, Fnet =0 because the wood block wasnt moving until 30 degrees.

The Attempt at a Solution

What I tried was drawing the free body diagram.
sin30=Fd/9.8m
cos30=Fn/9.8m

letting m=m, i get (Fd/sin30)=(Fn/cos30)

Substitute 0-Ff for Fd, and Ff/u for Fn.

this simplifies to -ucos30=sin30, giving u= -.577 or .577

Does this seem correct? I don't know what the right answer is but its odd that I got a negative answer and would love some confirmation that this is indeed correct ... or wrong :P

Thanks

 

[andrevdh]

note that when you say

Fnet = Fd + f

you do not include the sign for f the frictional force that is acting upwards in the opposite direction to the downwards component. When we add forces that work inline we take their direction into account. This means that you should actually say

0 = Fd - f

this implies that you chose downwards along the incline as the positive direction.

Some similar problems would require one to solve for an unknown force. If you were to get a negative value for its value it just means that your initial choice for its direction was wrong, it actually acts in the opposite direction.

Your value for the coefficient is correct.

 

[avsj]

Thanks andrevdh :D

 

[andrevdh]

Its a pleasure.