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Chapter 7: Problem 13
Is the principle of conservation of momentum always valid, or are therespecial conditions necessary for it to be valid? Explain.
Short Answer
Expert verified
Answer: The principle of conservation of momentum is valid for isolated systems, where no external forces are acting on the system. It is also valid during collisions between objects, regardless of the nature of the collision (elastic or inelastic). Kinetic energy conservation, however, may vary depending on the type of collision.
Step by step solution
01
Understanding the Principle of Conservation of Momentum
The principle of conservation of momentum states that when no external forces are acting on a system, the total momentum of that system remains constant. In mathematical terms, the conservation of momentum is represented by the equation:Total initial momentum = Total final momentumm1 * u1 + m2 * u2 = m1 * v1 + m2 * v2where m1 and m2 are the masses of the objects, u1 and u2 are their initial velocities, and v1 and v2 are their final velocities after the interaction.
02
Conservation of Momentum in Isolated Systems
The crucial condition for the conservation of momentum principle to be valid is that the system of objects should be isolated, meaning no external forces are acting on it. External forces like gravity, friction, and air resistance can affect the system's momentum. If external forces are acting on the system, the total momentum will change, and conservation of momentum will not be valid.
03
Conservation of Momentum During Collisions
In case of collisions between objects, we usually deal with conserved momentum. If the collision is elastic (no energy is lost, and the objects bounce off each other), both momentum and kinetic energy are conserved. In inelastic collisions (energy is lost, and the objects may stick together), only momentum is conserved but not the kinetic energy.#Conclusion#
04
Validity of Conservation of Momentum
The principle of conservation of momentum is valid only under specific conditions. It is valid for isolated systems, where no external forces are acting on the system. For collisions between objects, momentum conservation is valid regardless of the nature of the collision (elastic or inelastic). However, kinetic energy conservation may vary depending on the type of collision (conserved in elastic collisions, not conserved in inelastic collisions).
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