Is Elastic Collision Invariance Predictable Across All Inertial Frames?

In summary, elastic collisions between two particles are described as those in which kinetic energy is conserved. Using the Galilean velocity transformation equations, it can be shown that if a collision is elastic in one inertial reference frame, it will also be elastic in all other frames. However, it is unclear whether this result could have been predicted from the conservation of energy principle, as it is unclear whether energy is conserved in all inertial frames or just one's own frame."
  • #1
wumple
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Homework Statement


A collision between two particles in which kinetic energy is conserved is described as elastic. Show, using the Galilean velocity transformation equations, that if a collision is found to be elastic in one inertial reference frame, it will also be found to be elastic in all other such frames. Could this result have been predicted from the conservation of energy principle?



Homework Equations





The Attempt at a Solution



I don't have trouble with the first part - the part I don't understand is the last question - could the result of the invariance of elastic collisions have been predicted by the conservation of energy principle? I guess I don't know enough about what the conservation of energy principle says in regard to inertial frames. According to the principle, is energy conserved only in your own frame or in all inertial frames?
 
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  • #2
Is it the same quantity of energy in all frames? I think the answer to this last question is no, which would mean that the result of elastic collisions being invariant in all inertial frames could not have been predicted by the conservation of energy principle.
 

FAQ: Is Elastic Collision Invariance Predictable Across All Inertial Frames?

What is the concept of invariance in relation to elasticity?

The concept of invariance in relation to elasticity refers to the property of a material to maintain its shape and size when subjected to external forces. This means that the material will return to its original shape and size once the forces are removed.

What are the factors that affect the invariance of elasticity?

The invariance of elasticity can be affected by factors such as temperature, pressure, and the nature of the material itself. For instance, changes in temperature can cause materials to expand or contract, which can affect their elasticity. Similarly, the pressure applied to a material can also impact its invariance, as some materials may become more or less elastic under different pressures.

How is the invariance of elasticity measured?

The invariance of elasticity is typically measured using two parameters: Young's modulus and Poisson's ratio. Young's modulus measures a material's resistance to deformation under tensile or compressive forces, while Poisson's ratio measures how a material's lateral size changes when it is stretched or compressed.

What are some real-world applications of the invariance of elasticity?

The invariance of elasticity has numerous real-world applications, including in the construction industry for designing and building structures that can withstand external forces, in the manufacturing industry for producing durable and resilient products, and in the medical field for developing prosthetics and other medical devices that mimic the elasticity of human tissues.

Can the invariance of elasticity be altered or improved?

The invariance of elasticity can be altered or improved through various methods, such as heat treatment, introducing impurities, or combining different materials to create composites with desired elastic properties. These methods can change the microstructure of the material, which can affect its overall elasticity and invariance.

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