Relativistic Mass Increase of a Bullet

[benEzra]

(Geek mode on: Yes, I know physicists don't like the concept of "relativistic mass" and prefer to define mass as the invariant length of a particle's momentum four-vector. BUT, the concept of relativistic mass does have merit and application in some situations, including this one.)

SO, how much "mass" (in the Einsteinian sense) does a bullet gain due to its velocity?

I'll use a .223 Remington pushing a 55-grain bullet at 3250 fps. That's 3.56394 grams at 990.6 meters per second (and 1.748626 kJ of energy).

The Lorentz equations tell us that gamma for 990.6 meters per second is 1.000000000005459152744. So the bullet gains 1.94561e-11 grams of "relativistic mass" (that's 19.4561 picograms). So, at the muzzle, your bullet "weighs" 55.0000000003 grains.

FWIW, if 19.4561 picograms of matter were converted into energy in a matter-antimatter reaction, 1.748626 kJ of energy would be released--same as the kinetic energy of a bullet that gains that much mass relativistically.

Isn't physics neat?

(Geek mode off.)

[cpileri]

Forget expanding hollowpoints, all we need is a projectile that goes close to the speed of light!
(without turning into pure energy)
C-

[BigG]

OK, Ben. Put the Bud Light down and back away from the table!

[Yooper]

What are the weight tolerances of factory bullets in the manufacturing process? Physics is even more fun when it makes a difference!

[hksw]

Yeah but how much younger (less older) is it after its flight?

[R.H. Lee]

Showoff. I don't even understand the question.

[jefnvk]

Did you stay at a Holiday Inn Express last night

(Really gotta take physics one of these days)

[Sindawe]

OK benEzra, that works for the comparison 'tween a bullet at rest (moving through space along with gun, the shooter, the planet and the rest of the galaxy). How about the the bullet fired from the same .223 caliber weapon and one at 'absolute rest' (not moving through space AT ALL with comparison to the rest of the universe) and one fired from the gun moving along with all the other stuff in the universe.

[benEzra]

Yeah but how much younger (less older) is it after its flight?

By the same factor (gamma). So one second in "bullet time" would be 1.000000000005459152744 second of observer time, or one second of stationary observer time would be only 1/(1.000000000005459152744) of bullet time.

How about the the bullet fired from the same .223 caliber weapon and one at 'absolute rest' (not moving through space AT ALL with comparison to the rest of the universe) and one fired from the gun moving along with all the other stuff in the universe.

Tell me the velocity of the earth in relation to the absolute rest frame first...

[HankB]

benEzra - since you've been doing these calculations, maybe you can tell me how fast would the bullet have to move before its relativistic mass increase was sufficient to cause it to collapse into a black hole? And at that velocity, what rifling rate would be required to increase the spin to the point where we'd have a naked singularity?

[benEzra]

benEzra - since you've been doing these calculations, maybe you can tell me how fast would the bullet have to move before its relativistic mass increase was sufficient to cause it to collapse into a black hole?

I can't tell you why off the top of my head, but I don't think that can happen due to the dynamics of how the relativistic mass increase actually works. This may be one reason why physicists working in GR use the definition of mass as the length of the four-momentum vector, which is velocity-invariant. (The downside of this is that E=mc2 has to be modified to fit this formulation, as I recall.) If it could indeed happen, it would be way beyond my ability to calculate on a TI-81, anyway. The Lorentz transformations are simple algebra, but general relativistic effects involve some REALLY hairy math.

And at that velocity, what rifling rate would be required to increase the spin to the point where we'd have a naked singularity?

I dunno, even if the first premise were possible. I wonder if we could sign up Steven Hawking as an honorary THR member...

[Nathaniel Firethorn]

Forget expanding hollowpoints, all we need is a projectile that goes close to the speed of light!

One word for ya:

Lasers.

- pdmoderator

[Denver]

Now THAT'S Entertainment!

[TallPine]

Since the earth rotates (and revolves around the sun) in an easterly direction, firing the bullet towards the west would actually make it slow down from its speed "at rest" - though it would vary between day and night because during the day our rotational movement is opposite the (solar) orbital movement.

Then there is the solar movement around the galaxy and the movement of the galaxy around whatever it is moving around .....

[Wiley]

Physics: What yer Grandma gave ya fer an upset stomach.

Mole: A little furry critter that eats yer vegetable garden from underneath.

[S Roper]

Engineer mode. You said the bullet weighs 55 grains. That tells me you're only using two sig. figs. Therefore 55 + 0000000003 = 55.

[Bergeron]

Ooooooo.

I love physics smack downs.

FWIW, (remebering from Modern Physics), as an object increases is velocity relative to a frame of rest, it is it's momentum (for purposes of calculations) not nessicarily it's mass that increases. This is why you can't accelerate to the speed of light, as your momentum exponetiatlly increases.

Might be wrong though. Please correct if so.

[odysseus]

So, at the muzzle, your bullet "weighs" 55.0000000003 grains.

So what is your point? There is a .0000000003 grain gain in "mass" due to energy. Is there something interesting here? Am I missing something?

[misANTHrope]

FWIW, (remebering from Modern Physics), as an object increases is velocity relative to a frame of rest, it is it's momentum (for purposes of calculations) not nessicarily it's mass that increases. This is why you can't accelerate to the speed of light, as your momentum exponetiatlly increases.

Actually, the momentum of a moving object is simply the product of its mass and velocity, so p=m*v. Therefore, if you assume no relativistic mass increase, then momentum simply increases linearly forever. However, once you take into account relatavistic mass changes, mass is no longer constant as velocity changes, so momentum no longer increases linearly WRT velocity.

A better way to think of the difficulty with achieving high speeds is to look at the kinetic energy of an object. This is proportional to the square of the velocity: T=.5mv^2. As a result, in order to double the speed of an object, you have to bestow upon it four times the energy through some means. If you look at this in terms of, say, a rocket, you'd need roughly four times the fuel to achieve that doubling of speed. And that's not even taking into account relatavistic mass increase.

[Sleeping Dog]

Isn't the surface of the earth moving toward the east at a pretty good clip? So if you shoot east, the bullet mass would increase. But if you shoot west, it may decrease?

I think I'll have to drag a computer to the line in the next match.

Regards.

[benEzra]

Engineer mode. You said the bullet weighs 55 grains. That tells me you're only using two sig. figs. Therefore 55 + 0000000003 = 55.

You engineers...

OK, how about 55.000000000000 +/- 0.0000000000000000000001 grains?

[mhdishere]

Remember that all these measurements are from the standpoint of the shooter, not the bullet. If the bullet were conscious it wouldn't notice any increase in mass, nor would it notice time dillation (sp?). Just like if I travel near the speed of light for a month, at the end of the month I'm a month older by my measurements, but from the reference point of a person left behind thousands of years will have passed.

Also, regarding shooting east/west, the same thing holds, the bullets mass increases when measured from the earth's surface, which is stationary compared to the bullet. It doesn't matter that the earth's surface is moving with relation to other reference points, all reference points are equal. If you're measuring from, say, a satellite that's moving west as the same rate the earth is moving east, thereby becoming a stationary reference point, the bullet would be moving faster in reference to the satellite when fired west than when fired east, but from the point of reference of the earth the bullet is moving at the same speed.

There's no universal reference point that's defined as "Stationary", nor under Einstien's theory does there need to be, that's the basis of relativity, that all motion is measured in reference to some point which is defined as stationary. If you have two objects in relation to each other it doesn't matter which you choose to call stationary.

That's about the extent of my physics.

[Brasso]

Just like if I travel near the speed of light for a month, at the end of the month I'm a month older by my measurements, but from the reference point of a person left behind thousands of years will have passed.

So does this apply to light photons as well?

[Firethorn]

Forget Lasers, I want a hellbore.

Plasma charge fired at something like .9c down the vacuum left by the evacuation laser.

Does anybody know if that would be enough to induce fusion when it hit something more solid?

[Dave R]

Shooting east, shooting west, doesn't matter. Didn't yer physics prof let you know that it all depends upon the frame a reference? That's why you can pour coffee on an airplane going 500 mph over a spinning globe moving around the sun in a moving arm of the galaxy, which is flying away from the cetner of the universe. And in this case, the frame of reference is the SHOOTER!

That's what Einstien's Theory of Relativity says, anyway, right? Everything's relative...

I've been wondering why my .17 centerfire hits those whistle pigs so hard. Its all that extra mass those 25gr. bullets pick up cuz they're going so fast!

Mystery of "pink mist" solved.