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PhysicsClassical Physics

Elastic vs Inelastic Collision: Which Cases Conserve Kinetic Energy?

The first record is perfectly inelastic because the objects stick and kinetic energy falls from 27 J to 24 J. Records 2 and 3 conserve both momentum and kinetic energy, so they are perfectly elastic.

Question

Take rightward velocity as positive. For each one-dimensional collision record, calculate the total kinetic energy before and after the collision. Then identify which collisions are perfectly elastic.

  1. A 4.0 kg4.0\,\mathrm{kg} block at +3.0 m/s+3.0\,\mathrm{m/s} and an 8.0 kg8.0\,\mathrm{kg} block at +1.5 m/s+1.5\,\mathrm{m/s} move together afterward at +2.0 m/s+2.0\,\mathrm{m/s}.
  2. A 3.0 kg3.0\,\mathrm{kg} block at +6.0 m/s+6.0\,\mathrm{m/s} and a 5.0 kg5.0\,\mathrm{kg} block at +4.0 m/s+4.0\,\mathrm{m/s} move afterward at +3.5 m/s+3.5\,\mathrm{m/s} and +5.5 m/s+5.5\,\mathrm{m/s}, respectively.
  3. A 3.0 kg3.0\,\mathrm{kg} block at +3.0 m/s+3.0\,\mathrm{m/s} and a 2.0 kg2.0\,\mathrm{kg} block at −2.0 m/s-2.0\,\mathrm{m/s} move afterward at −1.0 m/s-1.0\,\mathrm{m/s} and +4.0 m/s+4.0\,\mathrm{m/s}, respectively.

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Evidence boundary

The calculations treat each record as an isolated one-dimensional system and include only translational kinetic energy. They classify the stated before-and-after states; they do not model deformation, heat, sound, rotation, or measurement uncertainty. ‘Perfectly inelastic’ is used only for the first record because the blocks stick together.