Suppose, in the first case, that an object (initially at rest in frame S) accelerates, for whatever reason upward, with a force F. Let M be the relativistic mass of the object.(adsbygoogle = window.adsbygoogle || []).push({});

The force measured in frame S is relativistically given by:

F_s=γ^2 M〖a_par〗^S+M〖a_ort〗^S

where 〖a_par〗^S is the accelration that is parrelel to the velocity and 〖a_ort〗^S is the accelration that is orthogonal to the velocity. IN this case, since the intial velocity is 0, the γ=0.

F_s= M(〖a_par〗^S +〖a_ort〗^S)

F_s= M (a^S)

Let frame S' exists as measured by an obesrver that travels say a velocity v downard.

The force measured in this frame must obey the same law, except that fact that all these measurements are in the S' reference frame.

F_s'=γ'^2 M〖a_par〗^S'+M〖a_ort〗^S'

the intial velocity is no longer 0 as this is in a nother frame of referce where the intial velocity is v. the force direction shouldnt be affected so it still points upward and the velocity measured in frame s' is upward. thus a_ort=0

F_s'=γ^2 M(a^S')

i can seperately proove that the realtivsitc mass does not vary in seeperate inertial frames of reference. taking the above statement as a matter of fact, even if it may not be true, just how can i figure out what (a^S') is in terms of (a^S) if the inertial motion is parrelel to the direction of accelration. i have an idea to take out such a calcluation and that is the follwoing

the observer in frame s measures the final velocity u^S after a time say t'. his meaurement of time is not the proper time since the locations at which he measures the velocities are different. the observer in frame S' should at that moment when the velocity of the particle is u^S meaure the velocity given by the realtivsitic addition of this vleocity as his realtive motion.

u^S'= (u^S + v)/ (1+(u^S*v)/c^2)

the time it took to reach that velocity in frame S' is not that same as in frame S. Notince how observer in frame s' meausres the proper time of the event as the location at which he examines the vlekocity occur at the same point. so frame s' meaures a time t.

the final velocity in frame S is beacuase of a_s

the final velocity in frame S' is because of a_s'

i cannot take out the mathematics of it.

can some1 tell me the solution

i think (if my work is coorect) i whould be getting something of this sort:

a_s'=a_s/ (1-v^2/c^2)

for the parrel case.

if the frame S' travels say to the right realtive to frame S (or the relative velocity is perp to the aaccelration, then i also want to know what the accelration across rframes is given the above formulations.)

thanks for some1 just tellin gme. i really need it

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# Acceleration measured in another inertial frame?

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