Two spheres collide and assume that the collision is perfectly elastic. Also --only linear momentum.(adsbygoogle = window.adsbygoogle || []).push({});

I have the relationship:

(va' - vb') dot N = -(va - vb) dot N

Where N is the normal vector at the point of collision. va and vb are initial velocities of object A and B, respectively. And va' and vb' are the final velocities of object A and B respectively.

I want to know how this relationship is derived.

This is what I try:

Relative to object B, object A has velocity v_ab. Relative to object B,

object B has velocity 0.

m_a*v_a + m_b*v_b = m_a*v_a' + m_b*v_b'

Relative to B:

m_a*v_ab + 0= m_a*v_ab' + 0

v_ab = v_ab'

That would give me this: (va' - vb') dot N = (va - vb) dot N

But I am missing the negative sign, because they should be opposite. Please

advise. Thanks in advance.

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# Two spheres collide and assume that the collision is perfectly elastic

**Physics Forums | Science Articles, Homework Help, Discussion**