Answer to Question #193087 in Mechanical Engineering for Gregory

Question #193087

the tensions of a flat belt are;right side 800n and slack side 300n. the angular speed n and diameter d of the pulley are 400 rev/min and 30cm respectively. if the coefficient of friction between the belt and the pulley is 0.7 and the mass of the belt is 2.1kg/m,including centrifugal tension, determine (a) initial tension of the belt (b) angle of lap in degrees (c) power transmitted (d) maximum power)


1
Expert's answer
2021-05-31T05:55:02-0400

"v = \\dfrac{\u03c0\u00d7d\u00d7\\omega}{60} = \\dfrac{400\u00d70.3\u00d7\u03c0}{60} = 6.28\\ m\/s"


"\\theta = tan^{-1} \\dfrac{800}{300}= 1.212\\ rad"



"\\dfrac{T_1}{T_2}= e^{\\mu\\theta}"


"T_2=\\dfrac{T_1}{e^{\\mu\\theta}}= \\dfrac{800}{e^{0.7\u00d7 1.212}}= 342.5N"


"P = (T_1-T_2)v =(800-342.5)\u00d7 6.28 = 2873.1W"

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