- #1
stevmg
- 696
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To yuiop:
Consider an object of mass m0 which, subjected to a constant force, accelerates at a0 initially. Initially, the velocity of this mass is zero but then picks up as this force is applied.
By the relativistic momentum equation,
a = dv/dt = a0[itex]\sqrt{(1 - v^2/c^2)}[/itex]
dv/[itex]\sqrt{(c^2 - v^2)}[/itex] = a0dt/c
sin-1 (v/c) = a0t/c
v/c = sin (a0t/c)
This is a periodic function (up and down depending on t) which is impossible
By your post
https://www.physicsforums.com/showpost.php?p=2864903&postcount=112
[itex]T_{a1} =\frac{c}{a_1}\, sinh(a_{a1} t_{a1}/c)[/itex]
[itex]v = \frac{a_1 T_{a1}}{\sqrt{1+(a_1 T_{a1}/c)^2}}[/itex]
How do I get my equation to equal your equations, or where is my mistake?
Consider an object of mass m0 which, subjected to a constant force, accelerates at a0 initially. Initially, the velocity of this mass is zero but then picks up as this force is applied.
By the relativistic momentum equation,
a = dv/dt = a0[itex]\sqrt{(1 - v^2/c^2)}[/itex]
dv/[itex]\sqrt{(c^2 - v^2)}[/itex] = a0dt/c
sin-1 (v/c) = a0t/c
v/c = sin (a0t/c)
This is a periodic function (up and down depending on t) which is impossible
By your post
https://www.physicsforums.com/showpost.php?p=2864903&postcount=112
[itex]T_{a1} =\frac{c}{a_1}\, sinh(a_{a1} t_{a1}/c)[/itex]
[itex]v = \frac{a_1 T_{a1}}{\sqrt{1+(a_1 T_{a1}/c)^2}}[/itex]
How do I get my equation to equal your equations, or where is my mistake?
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