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GR0177 #79
Problem
 GREPhysics.NET Official Solution Alternate Solutions
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Special Relativity}Rest Mass

The total relativistic energy is .
The total relativistic momentum is .

Plugging the momentum into the first equation, one has , as in choice (D).  Alternate Solutions
 Deafro2012-01-24 15:45:45 E^2=sqrt(p^2*c^2+(m*c^2)^2) E=10 GeV p=8 GeV/c mc^2= rest energy Rearrange the formula and solve for mc^2.Reply to this comment mike2009-11-06 18:34:27 Another way of doing it: and . Multiply the first eqn by and divide the two to get: Plug in to to find . Plug back in to the momentum equation: thus . I omit units, but it should be easy enough to follow. It seems a little longer, but its much less thinking once one remembers the relativistic energy/momenta equations. Reply to this comment Ning Bao2008-02-01 07:43:40 Set c=1 -> pythagorean triple.Reply to this comment Deafro
2012-01-24 15:45:45
E^2=sqrt(p^2*c^2+(m*c^2)^2)

E=10 GeV
p=8 GeV/c
mc^2= rest energy

Rearrange the formula and solve for mc^2. mike
2009-11-06 18:34:27
Another way of doing it:

and

. Multiply the first eqn by and divide the two to get:

Plug in to to find .

Plug back in to the momentum equation:

thus .

I omit units, but it should be easy enough to follow. It seems a little longer, but its much less thinking once one remembers the relativistic energy/momenta equations. astrodoo
2008-09-17 01:38:23
manasi, the value of 64 (<- the square of momentum) has a dimension of , so you can easily catch the yosun's solution if you consider the dimension of each terms. Ning Bao
2008-02-01 07:43:40
Set c=1 -> pythagorean triple. Gaffer
2007-10-24 08:42:58
There is a typo in the soln, which is why manasi is confused. Yosun used the to cancel the GeV/c in the momentum. But then she pulled it out again inthe next line.

No biggie.

It should go:

Plugging the momentum into the first equation, one has
and then continue as she concludes manasi
2007-09-28 12:05:48
hi, if i m not mistaken shudnt it be ????

hope it appears rite m new to latex!!
hey thanks a lot yosun.. ur solutions are very helpful!! :)
 astrodoo2008-09-17 01:46:59 manasi, the value of 64 (<- the square of the momentum) has a dimension of , so you can easily catch Yosun's solution in which term is disappeared if you look dimensions of each term.      LaTeX syntax supported through dollar sign wrappers $, ex.,$\alpha^2_0$produces . type this... to get...$\int_0^\infty\partial\Rightarrow\ddot{x},\dot{x}\sqrt{z}\langle my \rangle\left( abacadabra \right)_{me}\vec{E}\frac{a}{b}\$