A rope of length L and mass M is being pulled on a rough horizontal floor by a constant horizontal force F=M g. The force is acting at one end of the rope in the same direction as the length of the rope. The coefficient of kinetic friction between the rope and the floor is 1 / 2. If the tension at the midpoint of the rope is (M g/x), then find x.

Question

A rope of length L and mass M is being pulled on a rough horizontal floor by a constant horizontal force F=M g. The force is acting at one end of the rope in the same direction as the length of the rope. The coefficient of kinetic friction between the rope and the floor is 1 / 2. If the tension at the midpoint of the rope is (M g/x), then find x. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

a=(F-μ N/M)=(M g-0.5 M g/M)= g / 2

T-μ M g / 2=M a / 2 T-M g / 4=M g / 4 ⇒ T=M g / 2

a=MF−μN​=MMg−0.5Mg​=g/2 T−μMg/2=Ma/2 T−Mg/4=Mg/4 ⇒T=Mg/2

$a = \frac{F - μ N}{M} = \frac{M g - 0.5 M g}{M} = g /2$

$T - μ M g /2 = M a /2$
$T - M g /4 = M g /4$
$\Rightarrow T = M g /2$