*8–52. Beam AB has a negligible mass and thickness, and supports the 200-kg uniform block. It is pinned at A and rests on the to
p of a post, having a mass of 20 kg and negligible thickness. Determine the two coefficients of static friction at B and at C so that when the magnitude of the applied force is increased to P=300 N, the post slips at both B and C simultaneously.
1 answer:
Answer:
μ₁ = 0.1048
μ₂ = 0.1375
Explanation:
Using static equation can find in both point the moment and the forces so:
∑ M = F *d , ∑ F = 0
∑ M A = 0
N₁ * 3 - 200 * 9.81 * 1.5 = 0
N₁ = 981
∑ M y = 0
N₂ + 300 * ³/₅ - 981 - 20 * 9.81 = 0
N₂ = 997.2 N
∑ M C = 0
F₁ * 1.75 - 300 * ⁴/₅ * 0.75 = 0
F₁ = 102.86
∑ M B = 0
300 * ⁴/₅ * 1 - F₂ * 1.75 = 0
F₂ = 137.14 N
The Force F1 and F2 related the coefficients of static friction
F₁ = μ₁ * N₁ ⇒ 102.86 N = μ₁ * 981 ⇒ μ₁ = 0.1048
F₂= μ₂ * N₂ ⇒ 137.14 N = μ₂ * 997 ⇒ μ₂ = 0.1375
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