Three blocks A, B, and C of equal mass m are placed one over the other, one on a smooth horizont

step 1 In this problem I am drawing the diagram here first. So just look at it carefully. After that I

Three blocks A, B, and C of equal mass m are placed one over...

Three blocks $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ of equal mass $\mathrm{m}$ are placed one over the other, one on a smooth horizontal ground as shown in figure. Coefficient of friction between any two blocks of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ is $0.5$. What would be the maximum value of mass of block $D$ so that the blocks $A, B$ and $C$ move without slipping over each other? (A) $3 \mathrm{~m}$ (B) $5 \mathrm{~m}$ (C) $6 \mathrm{~m}$ (D) $4 \mathrm{~m}$

Three blocks $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ of equal mass $\mathrm{m}$ are placed one over the other, one on a smooth horizontal ground as shown in figure. Coefficient of friction between any two blocks of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ is $0.5$. What would be the maximum value of mass of block $D$ so that the blocks $A, B$ and $C$ move without slipping over each other?
(A) $3 \mathrm{~m}$
(B) $5 \mathrm{~m}$
(C) $6 \mathrm{~m}$
(D) $4 \mathrm{~m}$

Key Concepts

Force Transmission in Contact Systems

In systems where objects are in contact, forces such as friction and normal forces are transmitted from one object to the next. Analyzing how these forces are transmitted is key to understanding the overall motion. This concept helps in determining whether the friction at various interfaces is sufficient to keep the bodies moving together without slipping when subjected to external forces.

Newton's Second Law

Newton’s Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. When analyzing a multi-body system, this principle is applied to determine the acceleration of the entire system as well as the force distribution among the bodies, ensuring that the applied forces do not exceed the frictional limits.

Static Friction

Static friction is the force that resists the initial relative motion between two surfaces in contact. It is characterized by a coefficient that, when multiplied by the normal force between the surfaces, gives the maximum force available to prevent slipping. Understanding static friction is crucial in determining the conditions under which objects move together without sliding over one another.

Normal Force

The normal force is the perpendicular contact force exerted by a surface on an object resting on it. In systems with multiple stacked objects, the normal force acting at the interface between any two bodies is determined by the weight of the objects above the interface. This force is essential for calculating the maximum static friction available to prevent slipping.

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