Question

A belt/pulley system has tight side of 1000N, a slack side of 100N and a wrap angle of 500 degrees. The belt is just on the point of slipping. What is the cofficient of friction?

Answer 1

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

$\frac{T_1}{T_2}=e^{\mu\theta}\\\Rightarrow \frac{1000}{100}=e^{\mu\times 500\times \frac{\pi}{180}}\\\Rightarrow 10=e^{\mu\times 500\times \frac{\pi}{180}}$

Taking natural logs on both sides

$ln10=\mu\times 500\times \frac{\pi}{180}\\\Rightarrow \mu=\frac{ln10}{500\times \frac{\pi}{180}}=0.26386$

∴ Coefficient of friction is 0.26386