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Yakk · 02-15-2005, 01:03 PM

I thought the mass increase was due to kinetic energy buildup in the objects.

As you add kinetic energy to an object, it gains mass. The amount of velocity a given amount of energy represents is described by the Lorentz equation and E=MC^2.

In the case of a closed system, the if you get the kinetic energy from other energy in the system (gravitational potential energy), the energy total doesn't change, and hence the mass.

ie:
M_moving = M_0 * (1/sqrt(1-(v/c)^2))
M_kinetic = M_moving - M_0 (ie, the additional mass added by moving)
M_kinetic = M_0 * (1 - sqrt(1-(v/c)^2)) / sqrt(1-(v/c)^2)
E = MC^2
E_kinetic = M_kinetic * C^2
E_kinetic = C^2 * M_0 * (c - sqrt(c^2-v^2))/sqrt(c^2-v^2)
let C=1 lightsecond/second
E_kinetic = M_0 * (1 - sqrt(1-v^2))/sqrt(1-v^2)

IIRC the above equation, with v very small, approaches E_kinetic = 1/2 M_0 v^2 (unless I made some math errors!)

What is the Taylor series expansion of M_0 * (1 - sqrt(1-v^2))/sqrt(1-v^2)? If my math was right, it the lowest order power should be 1/2 M_0 v^2. With v << 1, higher order powers disappear compared to v^2.

I might be wrong, but that is how I thought of it.

Interestingly, for one object, a change in mass should have no change on the accelleration nor the velocity. However a change in mass in the other body would increase accelleration. If two bodies falling towards each other gained mass, they would accellerate faster, not slower, because of it. It wouldn't defend you against breaking light speed at all.

02-15-2005, 01:03 PM	#21 (permalink)
Yakk Wehret Den Anfängen! Location: Ontario, Canada	I thought the mass increase was due to kinetic energy buildup in the objects. As you add kinetic energy to an object, it gains mass. The amount of velocity a given amount of energy represents is described by the Lorentz equation and E=MC^2. In the case of a closed system, the if you get the kinetic energy from other energy in the system (gravitational potential energy), the energy total doesn't change, and hence the mass. ie: M_moving = M_0 * (1/sqrt(1-(v/c)^2)) M_kinetic = M_moving - M_0 (ie, the additional mass added by moving) M_kinetic = M_0 * (1 - sqrt(1-(v/c)^2)) / sqrt(1-(v/c)^2) E = MC^2 E_kinetic = M_kinetic * C^2 E_kinetic = C^2 * M_0 * (c - sqrt(c^2-v^2))/sqrt(c^2-v^2) let C=1 lightsecond/second E_kinetic = M_0 * (1 - sqrt(1-v^2))/sqrt(1-v^2) IIRC the above equation, with v very small, approaches E_kinetic = 1/2 M_0 v^2 (unless I made some math errors!) What is the Taylor series expansion of M_0 * (1 - sqrt(1-v^2))/sqrt(1-v^2)? If my math was right, it the lowest order power should be 1/2 M_0 v^2. With v << 1, higher order powers disappear compared to v^2. I might be wrong, but that is how I thought of it. Interestingly, for one object, a change in mass should have no change on the accelleration nor the velocity. However a change in mass in the other body would increase accelleration. If two bodies falling towards each other gained mass, they would accellerate faster, not slower, because of it. It wouldn't defend you against breaking light speed at all. __________________ Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.