QuestionMay 10, 2025

the sum of the kinetic energies of the objects in a system point masses inelastic collision conservation of momentum principle linear momentum isolated system internal kinetic energy change in momentum impulse perfectly inelastic collision elastic collision

the sum of the kinetic energies of the objects in a system point masses inelastic collision conservation of momentum principle linear momentum isolated system internal kinetic energy change in momentum impulse perfectly inelastic collision elastic collision
the sum of the kinetic energies of the objects in a system point masses inelastic collision conservation of momentum principle linear momentum isolated system internal kinetic energy change in momentum impulse perfectly inelastic collision elastic collision

Solution
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Answer

The sum of kinetic energies changes based on collision type: decreases in perfectly inelastic, conserved in elastic. Explanation 1. Define the System Consider an isolated system with point masses undergoing a collision. 2. Apply Conservation of Momentum In an isolated system, **momentum is conserved**. For two objects, m_1v_1 + m_2v_2 = m_1v'_1 + m_2v'_2, where v and v' are initial and final velocities. 3. Analyze Collision Type In a perfectly inelastic collision, objects stick together post-collision, minimizing kinetic energy. In elastic collisions, **kinetic energy is conserved**. 4. Calculate Internal Kinetic Energy Internal kinetic energy changes due to collision type. For perfectly inelastic, it decreases; for elastic, it remains constant. 5. Determine Impulse Impulse equals change in momentum: I = \Delta p = m(v' - v).

Explanation

1. Define the System<br /> Consider an isolated system with point masses undergoing a collision.<br /><br />2. Apply Conservation of Momentum<br /> In an isolated system, **momentum is conserved**. For two objects, $m_1v_1 + m_2v_2 = m_1v'_1 + m_2v'_2$, where $v$ and $v'$ are initial and final velocities.<br /><br />3. Analyze Collision Type<br /> In a perfectly inelastic collision, objects stick together post-collision, minimizing kinetic energy. In elastic collisions, **kinetic energy is conserved**.<br /><br />4. Calculate Internal Kinetic Energy<br /> Internal kinetic energy changes due to collision type. For perfectly inelastic, it decreases; for elastic, it remains constant.<br /><br />5. Determine Impulse<br /> Impulse equals change in momentum: $I = \Delta p = m(v' - v)$.
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