GREPhysics.NET: GR9677 #36

GR9677 #36

Problem

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Special Relativity $\Rightarrow$ }Conservation of Energy

The rest mass for each mass is 4kg. They collide head-on with identical speeds pointing in opposite directions. This implies that the composite mass is at rest. Thus, recalling that the total energy is given by $E=\gamma mc^2$ and that the rest mass is given by $E=mc^2$ , one has
$2\gamma mc^2 = Mc^2$ , where M is the composite mass.

The particle travels at $v=3c/5$ , which yields $\gamma = 5/4$ . Plug this in to get $M=10/4 \times 4 = 10kg$ .

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Comments

CaspianXI
2009-03-22 16:24:17

The two lumps' energies will be "converted" into mass when they collide and stop because we're given that no energy is radiated. Hence, the final mass must be greater than 8 kg. So, we can immediately eliminate options (A), (B), and (C).

So, if you can't figure it out, you can guess and have a 50% chance of getting it right.

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lowder.chris
2007-10-03 21:31:57

Relativity gives me a headache. :)

bbaker03
2007-10-16 18:38:25

sorry im looking at the solution and getting confused. are you using the equation $\gamma$ = $\1/sqrt{1-v^2/c^2}$

grae313
2007-10-31 12:44:17

yes, bbaker03, if you plug in $v = 3c/5$ to the equation you wrote for gamma, you get $\gamma = 5/4$

bbaker03
2007-11-01 10:24:11

Thanks a lot for your help this site is saving my life on this test. Can't thank you all enough.

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The two lumps' energies will be "converted" into mass when they collide and stop because we're given that no energy is radiated. Hence, the final mass must be greater than 8 kg. So, we can immediately eliminate options (A), (B), and (C). So, if you can't figure it out, you can guess and have a 50% chance of getting it right.

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