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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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