Suppose a moving body collides with another body and we are given the Young's Moduli of the two bodies. Is there any method to find their final velocities?
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1I have updated my answer to address the title of your post. Hope it helps. – Bob D Nov 13 '19 at 23:19
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Suppose a moving body collides with another body and we are given the Young's Moduli of the two bodies. Is there any method to find their final velocities?
Young's Modulus, or the modulus of elasticity, applies to linear elastic behavior of a deformable solid. If you are told that the collision between the objects is perfectly elastic, you then also know both kinetic energy and momentum are conserved and from that (and their masses and initial velocities) and you can determine the final velocities. You don't need Young's Modulus for that, just the equations for conservation of momentum and kinetic energy.
As far as the coefficient of restitution is concerned, knowing Young's Modulus alone does not tell you if the collision is perfectly elastic, meaning no loss of kinetic energy, unless you also know the actual stresses experienced by the objects during the collision reflect perfectly elastic behavior, then you will know that the coefficient of restitution, $ε$ = 1. If it is not elastic, knowing Young's Modulus will not help, because it only applies to elastic behavior. Then $0<ε<1$ for a partially inelastic collision where some kinetic energy lost, and $ε=0$ for a perfectly inelastic collision where the loss in kinetic energy is the maximum possible, consistent with conservation of momentum.
Hope this helps.
Bob D
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Let us suppose a ball collides with a wall in real world(and not in ideal world). Can we find the final velocity of the ball? – Rajarshi Misra Nov 15 '19 at 07:51
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@RajarshiMisra You can but you would need to know the coefficient of restitution or, equivalently, be told how much, if any, kinetic energy is lost. Then, ignoring the infinitesimal velocity of the wall/earth following the collision needed for conservation of momentum, you can determine the ball's velocity. – Bob D Nov 15 '19 at 11:49