Why Is µ Equal to tan θ in Friction Calculations?

[1010]

Homework Statement

Deriv µs = tan θ
For when a block is put on a wooden plank and the plank is lifted at one side.

Homework Equations

tan = sin/cos
Ff = µFn

The Attempt at a Solution

Ff = µFn
-mgsinθ= µ (-mgcosθ)
µ =(-mgsinθ) /(-mgcosθ)
µ = tan θ

Where i am confused is why Ff = -mgsinθ. Is it because the block has an acceleration of zero when falling down the plank?

 

[cristo]

Where i am confused is why Ff = -mgsinθ. Is it because the block has an acceleration of zero when falling down the plank?

Yes, the block is assumed not to move, and so the frictional force must balance the component of the weight of the block parallel to the plank.