Question

Помогите с решением задачи

Answer 1

Fт = μ·N

Вдоль оси Х: N₁ - μ₂N₂ = 0

Вдоль оси Y: μ₁N₁ + N₂ - mg - Mg = 0

Вокруг точки О: N₁·L·cos α + μ₁N₁·L·sin α - mg·L/2·sin α - Mg·h·tg α = 0

N₁ = μ₂N₂

μ₁·μ₂N₂ + N₂ = (m + M)·g

Mg·h·tg α = (N₁·cos α + μ₁N₁·sin α - mg/2·sin α)·L

N₁ = μ₂N₂

N₂·(1 + μ₁·μ₂) = (m + M)·g

Mg·h·tg α = (N₁·(cos α + μ₁·sin α) - mg/2·sin α)·L

N₂ = (m + M)·g/(1 + μ₁·μ₂)

N₁ = μ₂·(m + M)·g/(1 + μ₁·μ₂)

Mg·h·tg α = (μ₂·(m + M)·g·(cos α + μ₁·sin α)/(1 + μ₁·μ₂) - mg/2·sin α)·L

M·h·tg α = (μ₂·(m + M)·(cos α + μ₁·sin α)/(1 + μ₁·μ₂) - m/2·sin α)·L

h = (μ₂·(m + M)·(cos α + μ₁·sin α)/(1 + μ₁·μ₂) - m/2·sin α)·L/(M·tg α)

h = (0,5·(10 + 50)·(√3/3 + 0,3·0,5)/(1 + 0,3·0,5) - 10/2 · 0,5)·4/(50·√3/3) ≈ 3,3 м