Answer:
b) tan a = 3
Explanation:
Draw a free body diagram (see attached).
There are three forces acting on the insect. Weight downwards, normal force towards the center of the hemisphere, and friction tangent to the surface.
Sum of the forces in the radial direction:
∑F = ma
N − mg cos α = 0
N = mg cos α
Sum of the forces in the tangential direction:
∑F = ma
μN − mg sin α = 0
Substituting:
μ(mg cos α) − mg sin α = 0
μ cos α − sin α = 0
μ cos α = sin α
μ = tan α
The maximum possible value of the angle is such that its tangent is equal to the coefficient of friction.
