Two blocks of mass m are brought close to each other with a spring (mass negligible) compressed between then. The spring has potential energy 1/2kx2, where k and x are the force constant and the compression of the spring. The system is held together by a string (mass negligible) that opposes the outward force of the spring. When the string is cut, the spring expands to to its natural length (where it stores no more potential energy), and the two blocks fly apart with total kinetic energy equal to the potential energy that had been stored in the spring. In terms of the mentioned quantities, find the mass of the system before the string was cut. The image depicts two distinct states of a system composed of two masses, each labeled \( m \), connected by a compressed spring with negligible mass. The setup is represented in two stages:1. **Initial State (Top Diagram)**: - Two blocks, each with mass \( m \), are shown positioned on either side of a compressed spring. - The spring is held in compression by a string connecting the two masses. - The spring in this state is labeled as "compressed spring of negligible mass." 2. **Released State (Bottom Diagram)**: - The string is no longer present, indicating that it has been cut or released. - The spring is now in an uncompressed state, no longer exerting force on the masses. - Both masses \( m \) are depicted moving away from the spring in opposite directions. - The velocity of each mass is indicated by arrows labeled \( v \), pointing outward from the spring.This diagram illustrates the concept of conservation of momentum and energy in a system where a compressed spring is released. Initially, the potential energy stored in the spring is converted into kinetic energy, causing the blocks to move with equal magnitude velocities in opposite directions after the string is released.

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Two blocks of mass m are brought close to each other with a spring (mass negligible) compressed between then. The spring has potential energy 1/2kx², where k and x are the force constant and the compression of the spring. The system is held together by a string (mass negligible) that opposes the outward force of the spring. When the string is cut, the spring expands to to its natural length (where it stores no more potential energy), and the two blocks fly apart with total kinetic energy equal to the potential energy that had been stored in the spring. In terms of the mentioned quantities, find the mass of the system before the string was cut.

The image depicts two distinct states of a system composed of two masses, each labeled \( m \), connected by a compressed spring with negligible mass. The setup is represented in two stages:

1. **Initial State (Top Diagram)**:
- Two blocks, each with mass \( m \), are shown positioned on either side of a compressed spring.
- The spring is held in compression by a string connecting the two masses.
- The spring in this state is labeled as "compressed spring of negligible mass."

2. **Released State (Bottom Diagram)**:
- The string is no longer present, indicating that it has been cut or released.
- The spring is now in an uncompressed state, no longer exerting force on the masses.
- Both masses \( m \) are depicted moving away from the spring in opposite directions.
- The velocity of each mass is indicated by arrows labeled \( v \), pointing outward from the spring.

This diagram illustrates the concept of conservation of momentum and energy in a system where a compressed spring is released. Initially, the potential energy stored in the spring is converted into kinetic energy, causing the blocks to move with equal magnitude velocities in opposite directions after the string is released.

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