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Elastic Collision of Two Bodies in One Dimension: The Generalized Case

Elastic Collision of Two Bodies in One Dimension: The Generalized Case. Paul Robinson. Initial Conditions.

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Elastic Collision of Two Bodies in One Dimension: The Generalized Case

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  1. Elastic Collision of Two Bodies in One Dimension:The Generalized Case Paul Robinson

  2. Initial Conditions • Block 1, of mass m1, moves across a frictionless surface with speed v1i. It collides elastically with block 2, of mass m2, which is at rest. After the collision, block 1 moves with speed v1f, while block 2 moves with speed v2f. What are v1f and v2f?

  3. Part 1: Isolate v2f • Using the conservation of momentum, we isolate v2f in terms of the other variables.

  4. Part 2: Solve for v1f • Take our v2f expression, and plug it into the conservation of kinetic energy.

  5. Part 2 cont… • Now, take the updated KE equation and solve for v1f in terms of the given constants. First we cancel out, then group the v12 on one side, and then factor and cancel out again.

  6. Solve for v2f • Take the v1f expression and plug into the conservation of momentum equation. Then, simply solve for v2f

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