Answer to Question #202466 in Mechanical Engineering for Brian

Question #202466

 A flat belt, 8 mm thick and 100 mm wide transmits power between two pulleys, running at 1600 m/min. The mass of the belt is 0.9 kg/m length. The angle of lap in the smaller pulley is 165° and the coefficient of friction between the belt and pulley is 0.3. If the maximum permissible stress in the belt is 2 MN/m2, find : 1. maximum power transmitted ; and 2. initial tension in the belt


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Expert's answer
2021-06-04T04:54:02-0400

T1T2=eμθ=e0.3×2.88=2.372.a\frac{T1}{ T2}= e^{μθ} = e^{0.3×2.88}= 2.372 … … . a

Tc=mv2=0.9×(26.67)2=640NT_c = mv^2 = 0.9 × (26.67)^2 = 640N

T=σ×b×t=Tc+T12×106×0.1×0.008=640+T1T = σ × b × t = T_c + T_1 → 2 × 106 × 0.1 × 0.008 = 640 + T_1

T1=1600640T1=960N.bT_1 = 1600 − 640 → T_1 = 960N … … . b

sub a in b ∶

960T2=2.372T2=404.72N\frac{960}{ T2} = 2.372 → T_2 = 404.72N

P=(T1T2)×vP=(960404.72)×26.67=14809.3W=14.8kWP = (T_1 − T_2) × v → P = (960 − 404.72) × 26.67 = 14809.3W = 14.8kW

T=T1+T2+2Tc2=960+404.72+(2×640)2=1322.36NTₒ = \frac{T_1 + T_2 + 2T_c}{ 2} =\frac{ 960 + 404.72 + (2 × 640)}{ 2 }= 1322.36N

But when we use equation below , we get the same result which given for [Tₒ]

T=T1+T2+Tc2=960+404.72+6402=1002.36NTₒ = \frac{T_1 + T_2 + T_c}{ 2} = \frac{960 + 404.72 + 640}{ 2} = 1002.36N


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