Tru Physics

Inelastic Collisions

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Tru Physics
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Introduction

Inelastic collisions are a central concept in the study of physics, particularly in the field of mechanics. These types of collisions, where kinetic energy is not conserved, are crucial to understanding how objects interact with each other when they collide.

Definition of Inelastic Collisions

In an inelastic collision, the total kinetic energy of the system is not conserved, although the total momentum of the system is conserved. This is expressed by the following equations:

Momentum Conservation:

m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}

Kinetic Energy Not Conserved:

\dfrac{1}{2}m_1v_{1i}^2 + \dfrac{1}{2}m_2v_{2i}^2 \neq \dfrac{1}{2}m_1v_{1f}^2 + \dfrac{1}{2}m_2v_{2f}^2

where:

  • m_1 and m_2 are the masses of the two objects,
  • v_{1i} and v_{2i} are the initial velocities of the objects,
  • v_{1f} and v_{2f} are the final velocities after collision.

Perfectly Inelastic Collisions

A special case of inelastic collision is the perfectly inelastic collision, in which the two objects stick together and move as a single object after collision. The conservation of momentum for perfectly inelastic collision can be represented as:

m_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f

where v_f is the final common velocity of the two objects.

Understanding Energy Loss

In an inelastic collision, the “lost” kinetic energy is typically converted into other forms of energy such as heat, sound, or deformation energy (the energy required to change the shape of an object).

Applications of Inelastic Collisions

Inelastic collisions are prevalent in our everyday world. Examples include a car crash (where the cars crumple upon impact), a baseball being hit by a bat, and most forms of particle collision in the atomic and subatomic world. Understanding inelastic collisions is thus crucial to fields as diverse as transportation safety, sports science, and quantum physics.

Despite the complexity of inelastic collisions, they provide a crucial tool for understanding the physical world. By studying the conditions under which collisions occur, and the resulting changes in energy and momentum, scientists and engineers can design safer vehicles, more effective sports equipment, and more precise particle accelerators.

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