Why Is the Coefficient of Restitution Calculated as (Va - Vb)/(Vb - Va)?

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Homework Help Overview

The discussion revolves around the coefficient of restitution, specifically the formula (Va - Vb)/(Vb - Va). Participants are exploring the reasoning behind this formulation and its implications in the context of collisions in physics.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the orientation of the reference system and the notation used for initial and final velocities. There is a discussion about the implications of using different notations for velocities and the conditions under which the coefficient of restitution is defined.

Discussion Status

The conversation is ongoing, with participants offering insights into the reasoning behind the formula and the need for clarity in notation. Some guidance has been provided regarding the interpretation of the coefficient of restitution and the conditions that affect its calculation.

Contextual Notes

There are mentions of the need for careful consideration of initial and final velocities, as well as the potential for confusion arising from the notation used. The discussion acknowledges that the values of the coefficient of restitution should fall between 0 and 1, reflecting different types of collisions.

Gank
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Why is it that the co-efficient of restitution is given by

(Va - Vb)/(Vb - Va) and not (Va - Vb)/(Va - Vb)?
 
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Depends much on how you decide to orient the reference system... anyway pay attention that initial velocities and final velocities are not necessarily equal, therefore you have better using different notations (like Va and Vb for initial velocities of the two objects and Ua and Ub for final ones)... indeed in your notation the second case you wrote would give you one no matter what happens...
 
But why do I use the Va- vb and then in the denominator use Ub-Ua?
 
http://en.wikipedia.org/wiki/Coefficient_of_restitution

As far as I understand, you want to have a number between 0 and 1 (0 being the case in which one object stops, 1 being elastic collision)... then you have to do the ratio of the final relative velocities and initial relative velocities... this order is simply used to get two positive numbers... you could also put absolute values and get the same result with any order...
 

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