GR0177 #79
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Alternate Solutions |
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. | ![Alternate Solution - Unverified](/img/altsol-unverified.gif) | mike 2009-11-06 18:34:27 | Another way of doing it:
![\gamma m v = 8 /c](/cgi-bin/mimetex.cgi?\gamma m v = 8 /c)
and
. Multiply the first eqn by and divide the two to get:
![v = \frac{4}{5}c](/cgi-bin/mimetex.cgi? v = \frac{4}{5}c)
Plug in to to find .
Plug back in to the momentum equation:
![\frac{5}{3} m \frac{4}{5} c = 8 / c](/cgi-bin/mimetex.cgi?\frac{5}{3} m \frac{4}{5} c = 8 / c)
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. | ![Alternate Solution - Unverified](/img/altsol-unverified.gif) | Ning Bao 2008-02-01 07:43:40 | Set c=1 -> pythagorean triple. | ![Alternate Solution - Unverified](/img/altsol-unverified.gif) |
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Comments |
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. | ![Alternate Solution - Unverified](/img/altsol-unverified.gif) | mike 2009-11-06 18:34:27 | Another way of doing it:
![\gamma m v = 8 /c](/cgi-bin/mimetex.cgi?\gamma m v = 8 /c)
and
. Multiply the first eqn by and divide the two to get:
![v = \frac{4}{5}c](/cgi-bin/mimetex.cgi? v = \frac{4}{5}c)
Plug in to to find .
Plug back in to the momentum equation:
![\frac{5}{3} m \frac{4}{5} c = 8 / c](/cgi-bin/mimetex.cgi?\frac{5}{3} m \frac{4}{5} c = 8 / c)
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. | ![Alternate Solution - Unverified](/img/altsol-unverified.gif) | 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. | ![NEC](/img/nec.gif) | Ning Bao 2008-02-01 07:43:40 | Set c=1 -> pythagorean triple. | ![Alternate Solution - Unverified](/img/altsol-unverified.gif) | 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 ![\8^2 (c/c)^2 + m^2 c^4 = 10^2](/cgi-bin/mimetex.cgi?\8^2 (c/c)^2 + m^2 c^4 = 10^2)
and then continue as she concludes | ![Typo Alert!](/img/typo-unfixed.gif) | 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!! :)
astrodoo 2008-09-17 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.
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| ![NEC](/img/nec.gif) |
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