Question

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Answer 1

Answer:

Here we can use:fs = fs max = μs. N

because this is the angle at which the force of static friction equals its maximum value. Use a coordinate system with +x down the slope and +y perpendicular to the slope.

Split the force of gravity into x and y components.

Apply Newton's second law twice.

ΣFx = m ax = 0

ΣFy = m ay = 0

mg sin(θ) - fs = 0

N - mg cos(θ) = 0

mg sin(θ) = μs. N (1)

N = mg cos(θ) (2)

Substitute the second expression into the first:

mg sin(θ) = μs . mg cos(θ)

The factors of mg cancel. Re-arranging gives:

sin(θ)/cos(θ) = tan(θ) = μs

So, the coefficient of static friction is equal to the tangent of the angle at which the objects slide.

You are given with μs =sqrt(3) = tan(θ)

therefore angle theta = Tan^-1 (sqrt(3)) = 60 degrees

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