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Calculate the acceleration of the mass 12 kg shown in the set up of fig. also calculate the tension in the string connecting the 12kg mass the string are weightless and inextensible the pulleys are weightless and frictionless?
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Calculate the acceleration of the mass 12 kg shown in the set up of fi...
Understanding the Setup
In this scenario, we have a 12 kg mass hanging from a pulley system. We will analyze the forces acting on the mass to determine its acceleration and tension in the string.
Forces Acting on the 12 kg Mass
- Weight of the Mass: The gravitational force acting on the mass can be calculated as:
- Weight (W) = mass (m) × gravitational acceleration (g)
- W = 12 kg × 9.81 m/s² = 117.72 N (downward)
- Tension in the String: The tension (T) in the string opposes the weight of the mass.
Applying Newton's Second Law
According to Newton's second law, the net force acting on the mass is equal to the mass multiplied by its acceleration (a).
- Net Force Equation:
- Net Force = Weight - Tension
- ma = W - T
Substituting the values:
- 12a = 117.72 - T
Considering the System Dynamics
Assuming the mass is accelerating downwards, we need to express T in terms of a:
- Rearranging gives us:
- T = 117.72 - 12a
If there is another mass connected to this system (not provided), it will influence the overall acceleration. However, for just the 12 kg mass with no other weight, we can assume T = W when in equilibrium.
Calculating Acceleration and Tension
Assuming the mass is in free fall (no other mass counteracting):
- The acceleration (a) will equal gravitational acceleration (g) = 9.81 m/s².
- Tension (T) = 0 N as it is falling freely.
In a more complex scenario with additional masses, you would solve for 'a' and 'T' using the system of equations derived from the forces acting on all masses involved.
Conclusion
- Acceleration of the 12 kg Mass: 9.81 m/s² (if falling freely)
- Tension in the String: 0 N (if no other masses are present)
This concise analysis helps in understanding the dynamics in a pulley system under gravity.
In this scenario, we have a 12 kg mass hanging from a pulley system. We will analyze the forces acting on the mass to determine its acceleration and tension in the string.
Forces Acting on the 12 kg Mass
- Weight of the Mass: The gravitational force acting on the mass can be calculated as:
- Weight (W) = mass (m) × gravitational acceleration (g)
- W = 12 kg × 9.81 m/s² = 117.72 N (downward)
- Tension in the String: The tension (T) in the string opposes the weight of the mass.
Applying Newton's Second Law
According to Newton's second law, the net force acting on the mass is equal to the mass multiplied by its acceleration (a).
- Net Force Equation:
- Net Force = Weight - Tension
- ma = W - T
Substituting the values:
- 12a = 117.72 - T
Considering the System Dynamics
Assuming the mass is accelerating downwards, we need to express T in terms of a:
- Rearranging gives us:
- T = 117.72 - 12a
If there is another mass connected to this system (not provided), it will influence the overall acceleration. However, for just the 12 kg mass with no other weight, we can assume T = W when in equilibrium.
Calculating Acceleration and Tension
Assuming the mass is in free fall (no other mass counteracting):
- The acceleration (a) will equal gravitational acceleration (g) = 9.81 m/s².
- Tension (T) = 0 N as it is falling freely.
In a more complex scenario with additional masses, you would solve for 'a' and 'T' using the system of equations derived from the forces acting on all masses involved.
Conclusion
- Acceleration of the 12 kg Mass: 9.81 m/s² (if falling freely)
- Tension in the String: 0 N (if no other masses are present)
This concise analysis helps in understanding the dynamics in a pulley system under gravity.
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Calculate the acceleration of the mass 12 kg shown in the set up of fig. also calculate the tension in the string connecting the 12kg mass the string are weightless and inextensible the pulleys are weightless and frictionless?
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Calculate the acceleration of the mass 12 kg shown in the set up of fig. also calculate the tension in the string connecting the 12kg mass the string are weightless and inextensible the pulleys are weightless and frictionless? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Calculate the acceleration of the mass 12 kg shown in the set up of fig. also calculate the tension in the string connecting the 12kg mass the string are weightless and inextensible the pulleys are weightless and frictionless? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the acceleration of the mass 12 kg shown in the set up of fig. also calculate the tension in the string connecting the 12kg mass the string are weightless and inextensible the pulleys are weightless and frictionless?.
Calculate the acceleration of the mass 12 kg shown in the set up of fig. also calculate the tension in the string connecting the 12kg mass the string are weightless and inextensible the pulleys are weightless and frictionless? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Calculate the acceleration of the mass 12 kg shown in the set up of fig. also calculate the tension in the string connecting the 12kg mass the string are weightless and inextensible the pulleys are weightless and frictionless? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the acceleration of the mass 12 kg shown in the set up of fig. also calculate the tension in the string connecting the 12kg mass the string are weightless and inextensible the pulleys are weightless and frictionless?.
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