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Two masses as shown are suspended from a massless Pulley calculate the acceleration of the system when masses are left free?
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Two masses as shown are suspended from a massless Pulley calculate the...
Understanding the System
In a typical pulley system with two masses, the acceleration of the system can be calculated by considering the forces acting on each mass.
Let’s Define the Masses
- Mass 1 (m1): heavier mass
- Mass 2 (m2): lighter mass
Assuming m1 > m2, when released, m1 will accelerate downwards, and m2 will accelerate upwards.
Forces Acting on the Masses
- The gravitational force on m1: F1 = m1 * g
- The gravitational force on m2: F2 = m2 * g
- The tension in the rope: T
Net Force Calculation
- The net force acting on the system can be expressed as:
F_net = F1 - F2 = m1 * g - m2 * g
Applying Newton’s Second Law
- According to Newton’s second law, the total mass of the system is (m1 + m2).
- The formula to calculate acceleration (a) is:
a = F_net / (m1 + m2)
Acceleration Formula
- Substitute F_net:
a = (m1 * g - m2 * g) / (m1 + m2)
- Simplifying gives:
a = g * (m1 - m2) / (m1 + m2)
Conclusion
The acceleration of the system when the masses are released is determined by the difference in their weights and the total mass. This formula allows you to compute the acceleration directly, demonstrating how the gravitational force influences the motion of the masses in the pulley system.
In a typical pulley system with two masses, the acceleration of the system can be calculated by considering the forces acting on each mass.
Let’s Define the Masses
- Mass 1 (m1): heavier mass
- Mass 2 (m2): lighter mass
Assuming m1 > m2, when released, m1 will accelerate downwards, and m2 will accelerate upwards.
Forces Acting on the Masses
- The gravitational force on m1: F1 = m1 * g
- The gravitational force on m2: F2 = m2 * g
- The tension in the rope: T
Net Force Calculation
- The net force acting on the system can be expressed as:
F_net = F1 - F2 = m1 * g - m2 * g
Applying Newton’s Second Law
- According to Newton’s second law, the total mass of the system is (m1 + m2).
- The formula to calculate acceleration (a) is:
a = F_net / (m1 + m2)
Acceleration Formula
- Substitute F_net:
a = (m1 * g - m2 * g) / (m1 + m2)
- Simplifying gives:
a = g * (m1 - m2) / (m1 + m2)
Conclusion
The acceleration of the system when the masses are released is determined by the difference in their weights and the total mass. This formula allows you to compute the acceleration directly, demonstrating how the gravitational force influences the motion of the masses in the pulley system.
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Two masses as shown are suspended from a massless Pulley calculate the acceleration of the system when masses are left free?
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Two masses as shown are suspended from a massless Pulley calculate the acceleration of the system when masses are left free? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two masses as shown are suspended from a massless Pulley calculate the acceleration of the system when masses are left free? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two masses as shown are suspended from a massless Pulley calculate the acceleration of the system when masses are left free?.
Two masses as shown are suspended from a massless Pulley calculate the acceleration of the system when masses are left free? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two masses as shown are suspended from a massless Pulley calculate the acceleration of the system when masses are left free? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two masses as shown are suspended from a massless Pulley calculate the acceleration of the system when masses are left free?.
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