- #1
nullspace7
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Two spheres collide and assume that the collision is perfectly elastic. Also --only linear momentum.
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.
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.