Question

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)

Answer 1

$v = \dfrac{π×d×\omega}{60} = \dfrac{400×0.3×π}{60} = 6.28\ m/s$

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

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

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

$P = (T_1-T_2)v =(800-342.5)× 6.28 = 2873.1W$