Elastic Collisions
Elastic collisions are a class of interactions between objects such that, in addition to momentum being conserved, kinetic energy is also conserved. With these two rules at work, the velocity of objects involved in an elastic collision be determined. Herewith is a derivation:
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1 |
If momentum is conserved |
m1 v1 + m2 v2 =m1v1’ + m2v2’ |
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If KE is conserved |
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3 |
Multiply line 2 by 2 and regroup terms |
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4 |
Factor line 3 |
m1 (v1 – v1’)(v1+ v1’) = m2(v2’ –v2)(v2 + v2’) |
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5 |
Regroup line 1 |
m1 (v1 – v1’) = m2(v2’ –v2) |
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6 |
Divide line 4 by line 5 |
(v1+ v1’) = (v2 + v2’) |
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7 |
Solve lines 1 & 6 for v1’ & v2’ |
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