Answer:
θ = 21.8º
Explanation:
We can solve this exercise using Newton's conditions for equilibrium, in the attached we can see a diagram of the forces.
The most used coordinate system is an axis parallel to the plane (x axis) and an axis perpendicular to the plane (y axis), let's write Newton's equations on this axes
Y Axis
N- = 0
N =
X axis
fr - Wₓ = 0 (1)
Let's use trigonometry to find the normal ones
sin θ = Wₓ / W
cos θ = / W
Wx = W sin θ
= W cos θ
The friction force has the formula
fr = μ N
fr = μ (W cos θ)
We substitute in 1
μ mg cosθ = mg sin θ
μ cos θ = sin θ
tan θ = μ
θ = tan⁻¹ μ
calculate
θ = tan⁻¹ 0.40
θ = 21.8º
