# Block on an Incline with Varying Elevation

• Becca93
In summary, the conversation discusses a problem involving a block at rest on an inclined plane and the determination of the angle at which the block begins to slide. The conversation also includes a hint for calculating the acceleration of the block. The solution involves using the coefficients of static and kinetic friction, as well as the equations for force and acceleration. Ultimately, the correct angle is found to be 0.372°, and the mistake of using radians instead of degrees is identified.

#### Becca93

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