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Asked by Hari Last Modified
Answer As an experienced tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, addressing your question about the collision of two billiard balls, let's delve into it.
In this scenario, if the potential energy of two billiard balls depends solely on the separation distance between their centers, we are essentially discussing a situation where the force between the balls is conservative. When the force is conservative, it implies that mechanical energy (kinetic energy plus potential energy) is conserved throughout the interaction.
Now, in an elastic collision, both momentum and mechanical energy are conserved. Since we are assuming potential energy corresponds to the force during collision and that potential energy depends only on the separation distance between the balls' centers, if this potential energy is entirely converted into kinetic energy during the collision, then it follows that the collision is elastic.
This outcome aligns with the principle of conservation of mechanical energy in elastic collisions, where kinetic energy is converted from potential energy and vice versa, but the total mechanical energy remains constant.
Therefore, if the potential energy between the billiard balls is solely determined by their separation distance and the collision conserves mechanical energy, the collision between the billiard balls would be elastic.
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