GR0177 #32



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Comments 
physgre 20151015 08:09:27  坑爹啊，m不是动质量吗
PinkieSans 20181023 01:24:01 
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  neo55378008 20120323 12:05:47  You may have seen in a relativity course that you can make a right triangle out of rest mass, momentum, and total energy (this comes from the invariance of fourmomentum).
Using Pythagorean's formula
The good thing about the triangle is some times they'll give you numbers for a special triangle (i.e. rest mass of 3, momentum of 4, energy must be 5). Knowing your special triangles could save you some time!
neo55378008 20120323 12:09:47 
You can also work in units where c=1 just to make things faster

  QM320 20081105 20:40:21  In the original solution  what is ?
p014k 20090215 17:47:42 
\beta is v/c

  joshuacc1 20051202 23:50:42  There\'s a simpler way to answer this question...
E^2 = (pc)^2 + (mc^2)^2
E = 2mc^2 = sqrt((pc)^2 + (mc^2)^2)
4(mc^2)^2 = (pc)^2 + (mc^2)^2
3(mc^2)^2 = (pc)^2
pc = sqrt(3)mc^2
choice (D)
Walter 20080815 16:22:27 
This is a great solution, I've just laid it out again..
The question says the total energy is twice the rest energy, which gives
square that
Equating the two expressions for gives
make the subject and you get , answer D as required, and you never even went near a , and that's got to be a good thing.

istezamer 20091101 15:09:48 
lovely!! I solved it this way!! thanks! :D

testtest 20101106 16:31:13 
Even easier if you take c=1 :
or
just put the c back to get the answer.

 

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