WEBVTT

1
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Here is the problem: A 3 kg ball at 4 m/s hits a 1 kg ball at negative 2 m/s in a perfectly elastic head-on collision. Find both final velocities.

2
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One-dimensional collision; positive velocities point one way, negative the other.

3
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Total momentum before.

4
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Elastic collision: conserve momentum and kinetic energy.

5
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Kinetic energy before and after.

6
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So the answer is v₁ equals 1 m/s, v₂ equals 7 m/s (elastic; kinetic energy conserved).

7
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Momentum is conserved in every collision when no external force acts. Kinetic energy is conserved only in elastic collisions; in a perfectly inelastic collision the objects stick together and the maximum possible kinetic energy is converted to heat, sound and deformation.

8
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Momentum before 10 equals after 10 kg times m/s, which checks out.

9
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Kinetic energy before 26 equals after 26 J, which checks out.