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Published byNicholas Mason Modified over 3 years ago

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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

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

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Velocity transformation

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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 !

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

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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

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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 =

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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

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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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1. "the total momentum of the two balls is the same as it was before." 2. "each ball has the same momentum after the collision as it did before." 3. "each.

1. "the total momentum of the two balls is the same as it was before." 2. "each ball has the same momentum after the collision as it did before." 3. "each.

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