Question

A rope tied vertically to the ceiling is pulled to the right by a force perpendicular (90°) of the rope. The rope is tied to a wall with the rope forming a 120° angle counter-clockwise from the vertical rope.

Find the tension of the rope is F = 100 N

Answer 1

Given,

When the rope is at the right angle, then tension in the rope $(T)=0$

Let the tension in the string becomes T, when the angle becomes $120^\circ$

let the length of the string be l, now applying the conservation of energy

$mg\times l=\frac{1}{2}mv^2 +mgl\cos30$

$2(l-l\cos30 )= v^2$

Hence, net tension in the string

$T = 100 \cos 30 + \frac{mv^2}{l}$

$=50\sqrt(3)+2m(1-\frac{\sqrt{3}}{2})$