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Two blocks are connected by a spring.The combination is suspended,at rest,from a string attached to the ceiling ,as shown in figure .The string breaks suddenly.Immediately after the string breaks ,what is the initial downward acceleration of the upper block of mass 2m ?
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Two blocks are connected by a spring.The combination is suspended,at r...
Initial Analysis:
When the string breaks, the two blocks will separate due to the release of the tension force in the string. The upper block of mass 2m will experience an initial downward acceleration.
Free Body Diagram:
To analyze the situation, we need to draw a free body diagram for the upper block. The forces acting on the upper block are:
1. Gravitational force (mg) acting downwards.
2. Spring force (Fs) acting upwards.
3. Tension force (T) acting upwards before the string breaks.
Equation of Motion:
Since the upper block is experiencing an initial downward acceleration, we can write the equation of motion for the upper block as:
F_net = ma
where F_net is the net force acting on the block, m is the mass of the block, and a is the acceleration.
Net Force Calculation:
The net force acting on the upper block after the string breaks is given by the difference between the gravitational force and the spring force:
F_net = mg - Fs
The gravitational force is equal to the weight of the block:
mg = 2mg
Spring Force Calculation:
The spring force is given by Hooke's Law:
Fs = kx
where k is the spring constant and x is the displacement from the equilibrium position.
Since the spring is at its natural length when the string breaks, the displacement is zero and the spring force is also zero:
Fs = k * 0 = 0
Net Force Calculation (Continued):
Substituting the values of the gravitational force and the spring force into the equation of motion, we get:
F_net = 2mg - 0 = 2mg
Acceleration Calculation:
Now, we can calculate the acceleration of the upper block using the equation:
F_net = ma
2mg = 2ma
Canceling out the mass from both sides of the equation, we get:
g = a
Therefore, the initial downward acceleration of the upper block is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.
Final Conclusion:
When the string breaks, the upper block of mass 2m experiences an initial downward acceleration equal to the acceleration due to gravity. This occurs because the tension force in the string is no longer present to counteract the gravitational force acting on the block.
When the string breaks, the two blocks will separate due to the release of the tension force in the string. The upper block of mass 2m will experience an initial downward acceleration.
Free Body Diagram:
To analyze the situation, we need to draw a free body diagram for the upper block. The forces acting on the upper block are:
1. Gravitational force (mg) acting downwards.
2. Spring force (Fs) acting upwards.
3. Tension force (T) acting upwards before the string breaks.
Equation of Motion:
Since the upper block is experiencing an initial downward acceleration, we can write the equation of motion for the upper block as:
F_net = ma
where F_net is the net force acting on the block, m is the mass of the block, and a is the acceleration.
Net Force Calculation:
The net force acting on the upper block after the string breaks is given by the difference between the gravitational force and the spring force:
F_net = mg - Fs
The gravitational force is equal to the weight of the block:
mg = 2mg
Spring Force Calculation:
The spring force is given by Hooke's Law:
Fs = kx
where k is the spring constant and x is the displacement from the equilibrium position.
Since the spring is at its natural length when the string breaks, the displacement is zero and the spring force is also zero:
Fs = k * 0 = 0
Net Force Calculation (Continued):
Substituting the values of the gravitational force and the spring force into the equation of motion, we get:
F_net = 2mg - 0 = 2mg
Acceleration Calculation:
Now, we can calculate the acceleration of the upper block using the equation:
F_net = ma
2mg = 2ma
Canceling out the mass from both sides of the equation, we get:
g = a
Therefore, the initial downward acceleration of the upper block is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.
Final Conclusion:
When the string breaks, the upper block of mass 2m experiences an initial downward acceleration equal to the acceleration due to gravity. This occurs because the tension force in the string is no longer present to counteract the gravitational force acting on the block.
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Two blocks are connected by a spring.The combination is suspended,at r...
G is the ans...
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Two blocks are connected by a spring.The combination is suspended,at rest,from a string attached to the ceiling ,as shown in figure .The string breaks suddenly.Immediately after the string breaks ,what is the initial downward acceleration of the upper block of mass 2m ?
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