Question

A rope having a weight per unit length of 0.4 lb/ft is wound 2 1/2 times around a horizontal rod. Knowing that the coefficient of static friction between the rope and the rod is 0.30, determine the minimum length x of rope that should be left hanging if a 100-lb load is to be supported

Answer 1

Explanation:

Tension in the rope

$\begin{aligned}T_{1} &=0.4 \times x \\T_{2} &=100+0.4 \times 10 \\&=104\end{aligned}$

$M s=0.3$  ∅  $=2 \cdot 5(2 \pi)=5 \pi$

$\begin{aligned}\frac{T_{1}}{T_{2}}=e^{\mu \theta} & \Rightarrow \frac{104}{0.4 x}=e^{0.3(5 \pi)} \\& \Rightarrow x=2.34 \mathrm{H}\end{aligned}$

NOTE : Refer the image