Part one
a ladder rests against a vertical wall. there
is no friction between the wall and the ladder.
the coefficient of static friction between the
ladder and the ground is µ = 0.464 .
(use the picture to determine the answer)
identify the set of equations which is correct.
answer choices:
1. a1, b2, c3
2. a2, b2, c1
3. a1, b1, c1
4. a1, b2, c2
5. a1, b1, c2
6. a2, b1, c3
7. a2, b1, c2
8. a1, b2, c1
9. a1, b1, c3
10. a2, b1, c1

part two
determine the smallest angle θ for which the
ladder remains stationary.
answer in units of ◦

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°