A 27-kg chandelier hangs from a ceiling on a 4.0 m long vertical wire. What horizontal force should be applied to the chandelier to displace its position 2.4 m to one side in equilibrium? Find 2F.

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Geometry: wire = 4 m, horizontal shift = 2.4 m, so vertical = 4 2 − 2. 4 2 ​ = 3.2 m and tan θ = 3.2 2.4 ​ = 4 3 ​ Equilibrium: T cos θ = m g = 270 and T sin θ = F F = 270 tan θ = 270 × 4 3 ​ = 202.5 N 2 F = 405

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