# Block on an Incline with Varying Elevation

Homework Statement
Part one: A block is at rest on an inclined plane whose elevation can be varied. The coefficient of static friction is μs= 0.390, and the coefficient of kinetic friction is μk= 0.190. The angle of elevation θ is increased slowly from the horizontal. At what value of θ does the block begin to slide (in degrees)?

(Hint after getting it incorrect: mass*acceleration = sum of net forces in one direction. Use mu_s to calculate the frictional force for the moment when it starts to slide)

Part two: Evaluate the acceleration of the block.

The attempt at a solution

So,

Ff = μFn
Fn= mgcosθ
Fparallel = mgsinθ
Ff = μ(mgcosθ)

When the block begins to slide, the force of friction has to be equal to the force parallel, right? You have to overcome the static μ.

So,
Fparallel = Ff
mgsinθ = μmgcosθ

mg's would cancel, so

sinθ = μcosθ
sinθ/cosθ = μ
tanθ = μ

θ= tan^-1(0.390)

However, the answer I get is 0.372°, and that isn't correct.

For the second half,
ƩFnet = ma
Fparallel - Ff = ma
mgsinθ - mgcosθ = ma
gsinθ - gcosθ = a

There's a flaw in my method, I just don't know what it is. Anyone know how to help?

• PaperAirplane