# Finding theta on an incline plane

1. Feb 18, 2012

### jorcrobe

1. The problem statement, all variables and given/known data
A block is resting on a wooden plank. On one end of the plank is a hinge so the other end my be lifted to create and angle θ with respect to the horizontal. The plank has a coefficient of static friction of μs.
Using the sum of forces along the plank. Find the angle at which the block begins to move in terms of μs.

2. Relevant equations
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3. The attempt at a solution

I gathered that in order for the block to move, the force of static friction must be met, so I set the force of friction equal to the weight force pointing down the slope; thinking that these two must be at least equal for movement. So, I have:

Fw_parallelToSlope = mgsin(theta)
Ff_static = mgcos(theta) * μ

Setting equal to:
mgcos(theta) * μ = mgsin(theta)

(rearranged below for theta)
theta = atan(μ)

Thoughts? Thanks, and best wishes.

Last edited: Feb 18, 2012
2. Feb 18, 2012

### LawrenceC

Assuming that atan(mu) is arctan(mu), you've got it correct.