Answer:
0.26386
Explanation:
T₁ = Tight side tension = 1000 N
T₂ = Slack side tension = 100 N
θ = Wrap angle = 500° = 500π/180 radians
μ = Coefficient of friction
Belt tension theory
[tex]\frac{T_1}{T_2}=e^{\mu\theta}\\\Rightarrow \frac{1000}{100}=e^{\mu\times 500\times \frac{\pi}{180}}\\\Rightarrow 10=e^{\mu\times 500\times \frac{\pi}{180}}[/tex]
Taking natural logs on both sides
[tex]ln10=\mu\times 500\times \frac{\pi}{180}\\\Rightarrow \mu=\frac{ln10}{500\times \frac{\pi}{180}}=0.26386[/tex]
∴ Coefficient of friction is 0.26386
