Orac
there still seems to be quite a difference in the
energy found in the momentum between the three calcs.
lets assume we are using up the 50 MJ as the
rail gun accelerates the projectile down a
1 meter long track in 1 second.
1 Newton meter = 1 Joule
one joule is defined "mechanically", being the energy transferred to an object by the mechanical work of moving it a distance of 1 metre against a force of 1 newton.
p=mv
p = 5000 kg* 141.421 ms = 707,105 Nm = 707,105 J
p = 1000 kg* 316.227 ms = 316,227 Nm = 316,227 J
p = 1 kg* 10,000 ms = 10,000 Nm = 10,000 J
where has all the energy gone?
so from my last post we have the same exact energy
50MJ
that produces three different results when calculating
the three different momentums of the three different masses
and their three different velocities.
707,105 Nm = 707kJ
316,227 Nm = 316kJ
10,000 Nm = 10kJ
http://www.convertunits.com/from/newton+meter/to/jouleshouldn't the energies be the same?
why are the energies different?
in physics things are supposed to be proportional
when dealing with forces and energy and distances
and time and mass.
I don't like to use the kinetic energy formula for this
reason.
I prefer to use p=mv (momentum)
and f=mv (derived from the mass and velocity of an object)
and f=ma for the force that causes acceleration of a mass.
f=ma holds true
if I want to accelerate a 5000 kg object to
a velocity of 141.421 ms in 1 second over a
distance of 1 meter.
707,105 N = 5000 kg * 141.421 ms^2
but KE = .5 * m * v^2 does not hold true.
I would not need to supply 50MJ to accelerate
a 5000 kg object to a velocity of 141.421 ms
in 1 second over a distance of 1 meter.
if I did use 50MJ the 5000 kg object would accelerate
to 10000 ms in 1 second over a distance of 1 meter.
here too theres a really big difference.
lets just consider that the rail gun being described
in the article is extremely energy wasteful and that most of
the energy used up is converted into heat.
and the kinetic energy formula is not the way to find the
energy required to give an object its velocity because of
the energy lost during acceleration from friction and resistance.
energy that certainly hasn't gone into the object.
so since the physical world is more perfect than our
usage of math to predict how things move in it , I
suppose we just need to pick the math that seems
to be more valuable from the choices that we have.
or invent our own.
