Answer:
1. A1, B2, C3
2. 47.1°
Explanation:
Sum of forces in the x direction:
∑Fₓ = ma
f − Fᵥᵥ = 0
f = Fᵥᵥ
Sum of forces in the y direction:
∑Fᵧ = ma
N − W = 0
N = W
Sum of moments about the base of the ladder:
∑τ = Iα
Fᵥᵥ h − W (b/2) = 0
Fᵥᵥ h = ½ W b
Fᵥᵥ (l sin θ) = ½ W (l cos θ)
l Fᵥᵥ sin θ = ½ l W cos θ
The correct set of equations is A1, B2, C3.
At the smallest angle θ, f = Nμ. Substituting into the first equation, we get:
Nμ = Fᵥᵥ
Substituting the second equation into this equation, we get:
Wμ = Fᵥᵥ
Substituting this into the third equation, we get:
l (Wμ) sin θ = ½ l W cos θ
μ sin θ = ½ cos θ
tan θ = 1 / (2μ)
θ = atan(1 / (2μ))
θ = atan(1 / (2 × 0.464))
θ ≈ 47.1°
