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A centrifugal clutch has four shoes. When the clutch is at rest, each shoe is pulled against a stop by a spring so that it leaves a radial clearance of 10 mm between the shoe and the rim. The pull exerted by the spring is then 700 N. The mass centre of the shoe is 150 mm from the axis of the clutch. If the internal diameter of the rim is 500 mm, the mass of each shoe is 6 kg, the stiffness of each spring is 75 N/mm and the coefficient of friction between the shoe and the rim is 0.35; find the power transmitted by the clutch at 400 r.p.m.

Correct Answer: 3.439 kW
Given : n = 4 ; c = 10 mm ; S = 700 N ; r = 150 mm ; D = 500 mm or R = 250 mm = 0.25 m ; m = 6 kg ; s = 75 N/mm ; µ = 0.35 ; N = 400 r.p.m. or ω = 2 π × 400/60 = 41.89 rad/s r1 = r + c = 150 + 10 = 160 mm = 0.16 m Pc = m.ω2.r1 = 6 x (41.89)2 × 0.16 = 1684.58 N Ps = S + c.s = 700 + 10 x 75 = 1450 N F = µ (P¬c – Ps) = 0.35 (1684.58 – 1450) = 82.1 N T = n.F.R = 4 × 82.1 × 0.25 = 82.1 N-m Power transmitted (P) = Tω = 82.1 x 41.89 = 3439.31 W = 3.439 kW.

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