Activity: Mass is not Conserved

Groups are asked to analyze the following standard problem:

Two identical lumps of clay of (rest) mass m collide head on, with each moving at 3/5 the speed of light. What is the mass of the resulting lump of clay?

What students learn
  • Mass is energy.
  • Energy is conserved, but mass alone is not.

Prerequisite Knowledge

  • Definitions of the relativistic momentum 2-vector, relativistic momentum conservation, & rest energy.

Student Conversations

  1. We're not changing reference frames here, so there is no Lorentz transformation. Students may not realize that the resulting lump is at rest.
  2. Many students will recognize that this is a totall inelastic collision. Students will not really be comfortable with the idea that energy is conserved in this collision. Remind them that in classical physics kinetic energy is conserved for elastic collisions, but for inelastic collisions, the total energy (taking into account the thermal energies, rest energies, etc) is conserved (the universe doesn't lose energy in the interaction).
  3. The big take-home message is that the total mass in the collision is not conserved. The mass of final lump is not \(M=2m\). Some of the kinetic energy of the two initial lumps transforms into rest mass of the final lump.
  4. In this problem, the two lumps are moving at the same speed, so the \(\gamma\) factor is the same for the two initial lumps. \(\gamma = 1\) for the final lump. In general, each lump will have it's own \(\gamma\) factor based on it's speed relative to the lab frame.

Wrap-Up

  • Ask several students to present/defend their responses.
  • See also the discussion [[gsr>book:gsr:hwmass|in the text]].

Two identical lumps of clay of (rest) mass \(m\) collide head on, with each moving at 3/5 the speed of light.

What is the mass of the resulting lump of clay?


Learning Outcomes