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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 7.5 mm between the shoe and the rim. The pull exerted by the spring is then 600 N. The mass centre of the shoe is 120 mm from the axis of the clutch. If the internal diameter of the rim is 350 mm, the mass of each shoe is 5 kg, the stiffness of each spring is 60 N/mm and the coefficient of friction between the shoe and the rim is 0.2; find the speed of the centrifugal clutch, if the power transmitted is 40.168 kW.

Correct Answer: 800 r.p.m.
Given : n = 4 ; c = 7.5 mm ; S = 600 N ; r = 120 mm ; D = 350 mm or R = 175 mm = 0.175 m ; m = 5 kg ; s = 60 N/mm ; µ = 0.2; P = 40.168 kW = 40.168 x 103 W r1 = r + c = 120 + 7.5 = 127.5 mm = 0.1275 m Pc = m.ω2.r1 = 5 x (83.78)2 × 0.1275 = 4474.67 N Ps = S + c.s = 600 + 7.5 x 60 = 1050 N F = µ (Pc – Ps) = 0.2 (4474.67 – 1050) = 684.93 N T = n.F.R = 4 × 684.93 × 0.175 = 479.45 N-m Power transmitted (P) = Tω = 479.45 x ω 40.168 x 103 W = 479.45 x ω ω = 83.779 rad/s Therefore, N = 60 x ω / (2 π) = 800 r.p.m.

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