Is Newton's Law of Restitution Accurate for Eccentric Impacts?

In summary, there has been some confusion regarding the application of Newton's law of restitution in collisions between point objects and eccentric impacts. While it is generally understood that the law applies to points on rigid extended bodies, there have been suggestions to consider the velocities of the centres of mass instead. However, it seems that the correct approach is to use the normal components of the contact velocities for point objects.
  • #1
aim1732
430
2
I have used Newton's law of restitution without problem in collisions between point objects but there seems to be a problem in its application in eccentric impacts.
I have always thought it is applied to points on rigid extended bodies that come in contact during the collision for eccentric collisions.[applied here implying their velocities are considered in the equation--
(-velocity of separation/velocity of approach) = e ]
But I recently came across suggestions on this forum that velocities of centres of mass of the extended objects is to be considered instead. Am I getting it wrong? Regrets if I am asking a stupid question...
For reference here is the link to the thread:
https://www.physicsforums.com/showthread.php?t=435457"
 
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  • #2
aim1732 said:
I have used Newton's law of restitution without problem in collisions between point objects but there seems to be a problem in its application in eccentric impacts.
I have always thought it is applied to points on rigid extended bodies that come in contact during the collision for eccentric collisions.[applied here implying their velocities are considered in the equation--
(-velocity of separation/velocity of approach) = e ]
But I recently came across suggestions on this forum that velocities of centres of mass of the extended objects is to be considered instead. Am I getting it wrong?
I'd say that you are correct, as long as you mean the normal components of the contact velocities. (I haven't looked at that thread.) You'd only use the velocities of the centers of mass for point objects.
 
  • #3
I'd say that you are correct, as long as you mean the normal components of the contact velocities.
Yes I meant the normal components.

Thanks a lot!
 

FAQ: Is Newton's Law of Restitution Accurate for Eccentric Impacts?

What is Newton's Law of Restitution?

Newton's Law of Restitution is a physics principle that describes the behavior of colliding objects. It states that the ratio of the relative velocity of separation to the relative velocity of approach is constant for a given pair of objects. This ratio is known as the coefficient of restitution.

What is the formula for Newton's Law of Restitution?

The formula for Newton's Law of Restitution is e = v2 - v1 / u1 - u2, where e is the coefficient of restitution, v1 and v2 are the velocities after the collision, and u1 and u2 are the velocities before the collision.

How is Newton's Law of Restitution applied in real-world situations?

Newton's Law of Restitution is used in various fields, such as sports and engineering, to understand and predict the outcome of collisions. For example, it is used in analyzing the bounces of balls in sports like tennis and basketball, and in designing safety features in vehicles to reduce the impact of collisions.

What are the limitations of Newton's Law of Restitution?

Newton's Law of Restitution assumes that the colliding objects are rigid and that there is no energy lost due to factors such as friction and deformation. In real-world situations, these assumptions may not hold true, leading to inaccuracies in the predicted outcomes.

How does the coefficient of restitution affect the behavior of colliding objects?

The coefficient of restitution determines the elasticity of the collision. A higher coefficient of restitution indicates a more elastic collision, where the objects bounce off each other with less energy lost. A lower coefficient of restitution indicates a more inelastic collision, where the objects stick together after the collision with more energy lost.

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