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Three blocks A,B,C of equal mass m are placed one over the other on a smooth horizontal ground as shown. Coefficient of friction bet any two blocks of A,B,C is 1/2. The max value of mass of block D so that the blocks A,B,C move without slipping over each other is?
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Three blocks A,B,C of equal mass m are placed one over the other on a ...
Tension T in the string pulls the combined system that consists of 3 masses.
If T is the tension in the string, then we get acceleration a = T/(3m)
Hence mass of block-A moves due to the net pulling force F= (m x a - μ x m x g) = ( (T/3) - μ x m x g)
The required condition for the block-A not to slip is, F ≤ 0
hence (T/3) ≤ (μ x m x g)
since T = mD xg , we get mD ≤ 3 x μ x m
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Three blocks A,B,C of equal mass m are placed one over the other on a ...
Analysis:
To find the maximum value of the mass of block D, we need to consider the forces acting on each block and the conditions for the blocks to move without slipping over each other.
Conditions for blocks to move without slipping:
1. The net force on each block should be zero.
2. The torque about the point of contact between any two blocks should be zero.
Forces acting on each block:
1. Block A: The only force acting on block A is the force of friction between A and B. Let this force be FAB.
2. Block B: The forces acting on block B are the force of friction between B and A (FAB), and the force of friction between B and C (FBC).
3. Block C: The only force acting on block C is the force of friction between C and B. Let this force be FBC.
Calculating the maximum value of mass of block D:
To calculate the maximum value of mass of block D, we need to find the maximum value of the force of friction between any two blocks. Let's consider the force of friction between blocks A and B (FAB).
Maximum force of friction between blocks A and B:
The maximum force of friction between two objects can be calculated using the equation F = μN, where F is the force of friction, μ is the coefficient of friction, and N is the normal force.
The normal force between A and B can be calculated as NAB = mg, where m is the mass of each block and g is the acceleration due to gravity.
Therefore, the maximum force of friction between A and B is FAB = μNAB = μmg.
Conditions for blocks to move without slipping:
To satisfy the conditions for the blocks to move without slipping, we need to ensure that the net force on each block is zero and the torque about the point of contact between any two blocks is zero.
Net force on block A:
The net force on block A can be calculated as the difference between FAB and the force of friction between A and the ground (FAG).
Since the coefficient of friction between A and the ground is also 1/2, the force of friction between A and the ground is FAG = (1/2)NAG = (1/2)(mg) = (1/2)mg.
Therefore, the net force on block A is FA_net = FAB - FAG = μmg - (1/2)mg = (μ - 1/2)mg.
For block A to move without slipping, FA_net = 0, which implies μ - 1/2 = 0.
Therefore, the maximum value of the coefficient of friction (μ_max) between blocks A and B is 1/2.
Net force on block B:
The net force on block B can be calculated as the difference between FAB and FBC.
Since FAB = FBC = μmg, the net force on block B is FB_net = FAB - FBC = μmg - μmg = 0.
Therefore, the net force on block B is zero, satisfying the condition for block B to move without slipping.
Net force on block C:
The net force on block C can be calculated as the difference between FBC
To find the maximum value of the mass of block D, we need to consider the forces acting on each block and the conditions for the blocks to move without slipping over each other.
Conditions for blocks to move without slipping:
1. The net force on each block should be zero.
2. The torque about the point of contact between any two blocks should be zero.
Forces acting on each block:
1. Block A: The only force acting on block A is the force of friction between A and B. Let this force be FAB.
2. Block B: The forces acting on block B are the force of friction between B and A (FAB), and the force of friction between B and C (FBC).
3. Block C: The only force acting on block C is the force of friction between C and B. Let this force be FBC.
Calculating the maximum value of mass of block D:
To calculate the maximum value of mass of block D, we need to find the maximum value of the force of friction between any two blocks. Let's consider the force of friction between blocks A and B (FAB).
Maximum force of friction between blocks A and B:
The maximum force of friction between two objects can be calculated using the equation F = μN, where F is the force of friction, μ is the coefficient of friction, and N is the normal force.
The normal force between A and B can be calculated as NAB = mg, where m is the mass of each block and g is the acceleration due to gravity.
Therefore, the maximum force of friction between A and B is FAB = μNAB = μmg.
Conditions for blocks to move without slipping:
To satisfy the conditions for the blocks to move without slipping, we need to ensure that the net force on each block is zero and the torque about the point of contact between any two blocks is zero.
Net force on block A:
The net force on block A can be calculated as the difference between FAB and the force of friction between A and the ground (FAG).
Since the coefficient of friction between A and the ground is also 1/2, the force of friction between A and the ground is FAG = (1/2)NAG = (1/2)(mg) = (1/2)mg.
Therefore, the net force on block A is FA_net = FAB - FAG = μmg - (1/2)mg = (μ - 1/2)mg.
For block A to move without slipping, FA_net = 0, which implies μ - 1/2 = 0.
Therefore, the maximum value of the coefficient of friction (μ_max) between blocks A and B is 1/2.
Net force on block B:
The net force on block B can be calculated as the difference between FAB and FBC.
Since FAB = FBC = μmg, the net force on block B is FB_net = FAB - FBC = μmg - μmg = 0.
Therefore, the net force on block B is zero, satisfying the condition for block B to move without slipping.
Net force on block C:
The net force on block C can be calculated as the difference between FBC
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Three blocks A,B,C of equal mass m are placed one over the other on a smooth horizontal ground as shown. Coefficient of friction bet any two blocks of A,B,C is 1/2. The max value of mass of block D so that the blocks A,B,C move without slipping over each other is?
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Three blocks A,B,C of equal mass m are placed one over the other on a smooth horizontal ground as shown. Coefficient of friction bet any two blocks of A,B,C is 1/2. The max value of mass of block D so that the blocks A,B,C move without slipping over each other is? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Three blocks A,B,C of equal mass m are placed one over the other on a smooth horizontal ground as shown. Coefficient of friction bet any two blocks of A,B,C is 1/2. The max value of mass of block D so that the blocks A,B,C move without slipping over each other is? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three blocks A,B,C of equal mass m are placed one over the other on a smooth horizontal ground as shown. Coefficient of friction bet any two blocks of A,B,C is 1/2. The max value of mass of block D so that the blocks A,B,C move without slipping over each other is?.
Three blocks A,B,C of equal mass m are placed one over the other on a smooth horizontal ground as shown. Coefficient of friction bet any two blocks of A,B,C is 1/2. The max value of mass of block D so that the blocks A,B,C move without slipping over each other is? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Three blocks A,B,C of equal mass m are placed one over the other on a smooth horizontal ground as shown. Coefficient of friction bet any two blocks of A,B,C is 1/2. The max value of mass of block D so that the blocks A,B,C move without slipping over each other is? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three blocks A,B,C of equal mass m are placed one over the other on a smooth horizontal ground as shown. Coefficient of friction bet any two blocks of A,B,C is 1/2. The max value of mass of block D so that the blocks A,B,C move without slipping over each other is?.
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Three blocks A,B,C of equal mass m are placed one over the other on a smooth horizontal ground as shown. Coefficient of friction bet any two blocks of A,B,C is 1/2. The max value of mass of block D so that the blocks A,B,C move without slipping over each other is?, a detailed solution for Three blocks A,B,C of equal mass m are placed one over the other on a smooth horizontal ground as shown. Coefficient of friction bet any two blocks of A,B,C is 1/2. The max value of mass of block D so that the blocks A,B,C move without slipping over each other is? has been provided alongside types of Three blocks A,B,C of equal mass m are placed one over the other on a smooth horizontal ground as shown. Coefficient of friction bet any two blocks of A,B,C is 1/2. The max value of mass of block D so that the blocks A,B,C move without slipping over each other is? theory, EduRev gives you an
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