Re: Q about relativistic mass increase, starship
- From: Jim Black <fmlast3@xxxxxxxxxxxxxxxx>
- Date: Sun, 3 Feb 2008 12:42:05 -0800
On Sat, 2 Feb 2008 10:12:16 -0800 (PST), Randy Poe wrote:
On Feb 2, 1:23 am, giveitawhril2...@xxxxxxxxx wrote:
A warning is often given that if one wants to have a spaceship
travelling at relativistic speeds (usually to get to another star),
the ship's mass increases, making acceleration more difficult. But if
it where an antimatter propelled ship, with mass being turned into
energy, then wouldn't the mass increase be offset by the increased
energy released?
No. This is why the term "relativistic mass" is discouraged,
because it tends to lead to these kinds of misconceptions.
The idea of "relativistic mass" comes from the fact that the
momentum formula p = m*v is replaced with p = gamma*m*v where
gamma > 1. So a moving mass has more momentum
than mv, i.e. it "acts like" the mass is increased if you
want to think of momentum as (some mass) * v. But it doesn't act
that way in any other sense.
And in particular, the formulas F = m*a and K.E. = (1/2) m*v^2 no longer
hold, whether you use the relativistic mass or the invariant rest mass.
Thus the minimum energy required (ignoring the inefficiencies inherent in
rocket propulsion) to change velocity by a small amount dv is not
m_rel*v*dv, as the original poster might think, where
m_rel = m_rest / sqrt(1 - v^2/c^2)
is the relativistic mass. Instead, it would be
m_rest * v * dv / sqrt(1 - v^2/c^2)^3,
which increases with velocity faster than the relativistic mass does.
The gravitational
mass is still the original m.
Better: Using either mass in Netwon's law of gravity F = G*m1*m2/r^2 is
wrong.
The energy available from
annihilation with antimatter is still mc^2, where m is
the original, constant, rest mass.
- Randy
This is true of the energy released in the ship's frame, which is more
relevant for the rocket propulsion problem posed. It should be noted that
in other reference frames, the energy is in fact equal to the relativistic
mass times c^2.
--
Jim E. Black (domain in headers)
How to filter out stupid arguments in 40tude Dialog:
!markread,ignore From "Name" +"<email address>"
[X] Watch/Ignore works on subthreads
.
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