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| Chyrebulis
5th Post
 
New Customer
|  "Re(1):Anyone a physics wiz?"
, posted Sat 11 Oct 18:55
Digging out sophomore relativity book...
Basically what you need here is the Lorentz transformation used on momentum and the relativistic definition of total energy. According to speical relativity:
E^2 = p^2*c^2 + m^2*c^4
where E is energy, m is mass, p is momentum and c is the speed of light.
Everyone should recognize the form of this equation for a body with no momentum, thus giving on the mass energy (i.e. E = mc^2).
However, we also need the relativistic relation between momentum and velocity which is:
p' = m*v' / sqrt(1 - v^2/c^2)
where p' is momentum in the direction you are trying to find (i.e. x,y, or z, m is mass, v' is the velocity along the same direction. v is the total velocity in all directions, an c is the speed of light.
In one-dimension you should only need that equation once. If you are moving in 2 or 3 dimaensions you will need to use equations breaking up p and v in the x,y or x,y,z components respectively.
With those equations I think you can do what your looking for. Hope that helps.
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| Gen 2053th Post
Platinum Carpet V.I.P- Board Master
    
    
    
    
   
| "Re(2):Anyone a physics wiz?" , posted Sat 11 Oct 20:09
quote:
Digging out sophomore relativity book...
Basically what you need here is the Lorentz transformation used on momentum and the relativistic definition of total energy. According to speical relativity:
E^2 = p^2*c^2 + m^2*c^4
where E is energy, m is mass, p is momentum and c is the speed of light.
Everyone should recognize the form of this equation for a body with no momentum, thus giving on the mass energy (i.e. E = mc^2).
However, we also need the relativistic relation between momentum and velocity which is:
p' = m*v' / sqrt(1 - v^2/c^2)
where p' is momentum in the direction you are trying to find (i.e. x,y, or z, m is mass, v' is the velocity along the same direction. v is the total velocity in all directions, an c is the speed of light.
In one-dimension you should only need that equation once. If you are moving in 2 or 3 dimaensions you will need to use equations breaking up p and v in the x,y or x,y,z components respectively.
With those equations I think you can do what your looking for. Hope that helps.
Ah!
Thanks this is good stuff.
How do you calculate the velocity in all directions? some kind of loci trig?
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| Chyrebulis
7th Post
New Customer
| "Re(5):Anyone a physics wiz?" , posted Sat 11 Oct 20:40
quote:
"p' = m*v' / sqrt(1 - v^2/c^2)
where p' is momentum in the direction you are trying to find (i.e. x,y, or z, m is mass, v' is the velocity along the same direction. v is the total velocity in all directions, an c is the speed of light."
doesn't
p' = m*v'
?
would the velocity in the opposite direction be the negative velocity
is velocity in all directions the sum of velocity in every direction?
it's a rocket on a 2D plain
thanks
p = m*v for non-relativistic (i.e. normal slow) speed. Once you start enterining the realm of relativity you need to include that extra term. Note it is that term (called the Lorentz transformation) which creates the acceleration phenomenon which you noted earlier. As v approaches c the denominator becomes very small and thus a very large increase in p (and therefore E) is needed to increase v.
Even if your rocket is in a 2-d plain, if there are no other forces (i.e. gravity, side thrusters, collisions, etc.) you should be able to reorient the coordinate system such that the direction of travel lies along the path of the rocket. For example, calling the path of the rocket the x axis.
When I say the total velocity I mean positive velocity. Although the "velocity" in the opposite direction is technically negative that is a trival result. So for example, if the rocket is traveling 3x10^7 m/s in the x direction, and 4x10^7 m/s in the y direction its total velocity should be 5x10^7 m/s.
Chyrebulis-sensei out...
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| Gen 2056th Post
Platinum Carpet V.I.P- Board Master
| "Re(6):Anyone a physics wiz?" , posted Sat 11 Oct 20:55
quote:
"p' = m*v' / sqrt(1 - v^2/c^2)
where p' is momentum in the direction you are trying to find (i.e. x,y, or z, m is mass, v' is the velocity along the same direction. v is the total velocity in all directions, an c is the speed of light."
doesn't
p' = m*v'
?
would the velocity in the opposite direction be the negative velocity
is velocity in all directions the sum of velocity in every direction?
it's a rocket on a 2D plain
thanks
p = m*v for non-relativistic (i.e. normal slow) speed. Once you start enterining the realm of relativity you need to include that extra term. Note it is that term (called the Lorentz transformation) which creates the acceleration phenomenon which you noted earlier. As v approaches c the denominator becomes very small and thus a very large increase in p (and therefore E) is needed to increase v.
Even if your rocket is in a 2-d plain, if there are no other forces (i.e. gravity, side thrusters, collisions, etc.) you should be able to reorient the coordinate system such that the direction of travel lies along the path of the rocket. For example, calling the path of the rocket the x axis.
When I say the total velocity I mean positive velocity. Although the "velocity" in the opposite direction is technically negative that is a trival result. So for example, if the rocket is traveling 3x10^7 m/s in the x direction, and 4x10^7 m/s in the y direction its total velocity should be 5x10^7 m/s.
Chyrebulis-sensei out...
OK thanks
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