Introduction to Classical Mechanics · Problem 12.22

4-vectors — Morin

Physics — Mechanics · cm-frame

Problem

CM frame ** A mass

m

travels at speed

3c/5

, and another mass

m

sits at rest. (a) Find the energy and momentum of the two particles in the lab frame. (b) Find the speed of the CM of the system, by using a velocity-addition argument. (c) Find the energy and momentum of the two particles in the CM frame, without using the Lorentz transformations. (d) Verify that the

E

's and

p

's are related by the relevant Lorentz transformations. (e) Verify that

E^2 - p^2c^2

for each mass is the same in both frames. Likewise for

E^2_{\text{total}} - p^2_{\text{total}}c^2

Related theory

Circling Stick Cm Frame Analysis

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