1. Mass, Energy, and Momentum In Relativity, Momentum = mu (u = speed in frame) Where m = m o u u V S S

2. Relative velocity Why the change in mass? Consider the relative velocities between frames: u S S u V

3. Velocity transformation

4. Mass, Energy, and Momentum u u V S S If u =.9c, and v =.9c, Using Galilean Relativity, u = 1.8c…not allowed! then u =.994c !

5. Now Consider a two body collision View Collision from Frame S: V S final S initial m momo M Combining gives:

6. Consider a two body collision View Collision from Frame S moving with velocity V=u relativie to S, so that M is at rest. S final S initial m m M uu Vm momo M

7. Proof that m= m 0 S fi nal S initi al m m M uu V S fin al S initia l m momo M Now that we have our velocities properly tranformed, lets combine the results of momentum conservation in frame S with the velocity transform equation between S and S: Namely V =

8. Proof that m= m 0 S fi nal S initi al m m M uu V S fin al S initia l m momo M

9. Simplifying: S fi nal S initi al m m M uu V S fin al S initia l m momo M