Question

A block of mass 2m is pulled along a horizontal frictionless surface by a rope of mass m. If force applied to the free end of the rope is F, then tension in the midpoint of the rope is

Answer 1

A block of mass 2m is pulled along a horizontal frictionaless surface by a rope of mass m.

If the applied force to the free end of the rope is D, then tension in the midpoint of the rope is..

let the system of mass and rope is moving with acceleration a by applying force F.

from Newton's 2nd law of motion,

$F=M_{total}\times a$

⇒ F = (2m + m) × a = 3ma

⇒$a=\frac{F}{3m}$

since we need to find the tension in the midpoint of the rope, mass of each part of the rope will be m/2.

let T is the tension in the midpoint of the rope.

for mass 2m and the part which is attached to the mass,

(2m + m/2) × a = T ,

from equation (1) we get,

⇒$\frac{5m}{2}\times\frac{F}{3m}=T$

⇒$T=\frac{5F}{6}$

Therefore the tension in the midpoint of the rope is 5F/6.