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

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

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

Velocity transformation

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 !

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

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

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 =

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

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

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