A rope of length L and mass M is being pulled | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) $1$. First,calculate the acceleration of the entire rope. The net force acting on the rope is $F_{net} = F - f_k$,where $f_k = \mu N = \mu Mg = (1

Vedclass · Accepted Answer

$\frac{Mg}{2}$

Vedclass · Answer

(D) $1$. First,calculate the acceleration of the entire rope. The net force acting on the rope is $F_{net} = F - f_k$,where $f_k = \mu N = \mu Mg = (1/2)Mg$. $2$. Thus,$F_{net} = Mg - 0.5Mg = 0.5Mg$. $3$. The acceleration $a$ is given by $a = F_{net} / M = 0.5Mg / M = g/2$. $4$. Now,consider the rear half of the rope (mass $M/2$). The forces acting on this half are the tension $T$ at the midpoint pulling it forward and the kinetic friction $f_k'$ pulling it backward. $5$. The friction on the rear half is $f_k' = \mu (M/2)g = (1/2)(M/2)g = Mg/4$. $6$. Applying Newton's second law to the rear half: $T - f_k' = (M/2)a$. $7$. Substituting the values: $T - Mg/4 = (M/2)(g/2) = Mg/4$. $8$. Therefore,$T = Mg/4 + Mg/4 = Mg/2$.

Similar Questions

$A$ man slides down a telegraphic pole with an acceleration equal to one-fourth of the acceleration due to gravity. The frictional force between the man and the pole is equal to which of the following in terms of the man's weight $w$?

$A$ block of mass $M = 5\,kg$ is resting on a rough horizontal surface for which the coefficient of friction is $0.2$. When a force $F = 40\,N$ is applied at an angle of $30^\circ$ with the horizontal,the acceleration of the block will be ........ $m/s^2$ $(g = 10\,m/s^2)$.

$A$ man of mass $60 \, kg$ slides down a pole by applying a force of $600 \, N$ on it. If the coefficient of friction between the hands and the pole is $0.5$,then the acceleration of the man is ............ $m/s^2$ $(g = 10 \, m/s^2)$.

$A$ $1\,kg$ block is being pushed against a wall by a force $F = 75\,N$ as shown in the Figure. The coefficient of friction is $0.25.$ The magnitude of acceleration of the block is ........ $m/s^2$. (Take $g = 10\,m/s^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module