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A system consists of two identical blocks, each of mass m connected by a massless spring of force constant k. Initially the system is in equilibrium as shown in the figure. The further compression that must be provided to the spring such that the lower block just lifts off the ground is ?
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A system consists of two identical blocks, each of mass m connected by...
Analysis:
To solve this problem, we can use the concept of equilibrium and the conditions for an object to lift off the ground.
Conditions for an object to lift off the ground:
For the lower block to lift off the ground, the net force acting on it in the upward direction should be equal to zero. In other words, the weight of the lower block should be balanced by the force exerted by the spring.
Equilibrium of the system:
In the given system, the two identical blocks are at rest and in equilibrium. This means that the net force and net torque acting on each block are zero.
Net force on each block:
The net force on each block is the sum of the weight and the force exerted by the spring. Since the two blocks are identical, the net force on each block is the same.
Force exerted by the spring:
The force exerted by the spring can be calculated using Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. In this case, the displacement is the compression of the spring.
Calculating the force exerted by the spring:
Let's assume that the compression of the spring is x. The force exerted by the spring on each block is given by F = kx, where k is the force constant of the spring.
Weight of each block:
The weight of each block is given by W = mg, where m is the mass of each block and g is the acceleration due to gravity.
Equilibrium condition:
For the lower block to lift off the ground, the net force on it should be equal to zero. This means that the force exerted by the spring should balance the weight of the block.
Setting up the equation:
The force exerted by the spring is equal to the weight of the block. Therefore, we can write the equation as kx = mg.
Solving for the compression:
To find the compression x, we can rearrange the equation as x = mg/k.
Conclusion:
The further compression that must be provided to the spring such that the lower block just lifts off the ground is mg/k. This means that the spring needs to be compressed by an amount equal to the weight of the block divided by the force constant of the spring.
To solve this problem, we can use the concept of equilibrium and the conditions for an object to lift off the ground.
Conditions for an object to lift off the ground:
For the lower block to lift off the ground, the net force acting on it in the upward direction should be equal to zero. In other words, the weight of the lower block should be balanced by the force exerted by the spring.
Equilibrium of the system:
In the given system, the two identical blocks are at rest and in equilibrium. This means that the net force and net torque acting on each block are zero.
Net force on each block:
The net force on each block is the sum of the weight and the force exerted by the spring. Since the two blocks are identical, the net force on each block is the same.
Force exerted by the spring:
The force exerted by the spring can be calculated using Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. In this case, the displacement is the compression of the spring.
Calculating the force exerted by the spring:
Let's assume that the compression of the spring is x. The force exerted by the spring on each block is given by F = kx, where k is the force constant of the spring.
Weight of each block:
The weight of each block is given by W = mg, where m is the mass of each block and g is the acceleration due to gravity.
Equilibrium condition:
For the lower block to lift off the ground, the net force on it should be equal to zero. This means that the force exerted by the spring should balance the weight of the block.
Setting up the equation:
The force exerted by the spring is equal to the weight of the block. Therefore, we can write the equation as kx = mg.
Solving for the compression:
To find the compression x, we can rearrange the equation as x = mg/k.
Conclusion:
The further compression that must be provided to the spring such that the lower block just lifts off the ground is mg/k. This means that the spring needs to be compressed by an amount equal to the weight of the block divided by the force constant of the spring.
Community Answer
A system consists of two identical blocks, each of mass m connected by...
Figure kahan hai?
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A system consists of two identical blocks, each of mass m connected by a massless spring of force constant k. Initially the system is in equilibrium as shown in the figure. The further compression that must be provided to the spring such that the lower block just lifts off the ground is ?
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A system consists of two identical blocks, each of mass m connected by a massless spring of force constant k. Initially the system is in equilibrium as shown in the figure. The further compression that must be provided to the spring such that the lower block just lifts off the ground is ? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A system consists of two identical blocks, each of mass m connected by a massless spring of force constant k. Initially the system is in equilibrium as shown in the figure. The further compression that must be provided to the spring such that the lower block just lifts off the ground is ? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system consists of two identical blocks, each of mass m connected by a massless spring of force constant k. Initially the system is in equilibrium as shown in the figure. The further compression that must be provided to the spring such that the lower block just lifts off the ground is ?.
A system consists of two identical blocks, each of mass m connected by a massless spring of force constant k. Initially the system is in equilibrium as shown in the figure. The further compression that must be provided to the spring such that the lower block just lifts off the ground is ? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A system consists of two identical blocks, each of mass m connected by a massless spring of force constant k. Initially the system is in equilibrium as shown in the figure. The further compression that must be provided to the spring such that the lower block just lifts off the ground is ? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system consists of two identical blocks, each of mass m connected by a massless spring of force constant k. Initially the system is in equilibrium as shown in the figure. The further compression that must be provided to the spring such that the lower block just lifts off the ground is ?.
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