Does an Object in a Vacuum Accelerate Indefinitely?

[easily confused]

okay, so i have two questions. the first one is, since there is no terminal velocity in a vacuum (this is true, right?), would an object continue to accelerate indefinitely? or is there some other force that would stop the acceleration at some point?

also, since symmetry dictates that a body that travels upwards through space must take the same amount of time to travel downwards through space (this is also true i think?), then if a bullet were shot straight up in the air, would it be just as deadly on the way back down as on the way up?

my husband and i launched into a huge debate over these simple physics laws, and since our combined distance from high school physics is almost 20 years, we figured we should probably consult someone who knows what they are talking about

 

[ArmoSkater87]

Thats a good question, i didnt know terminal velocity is caused by air resistnace. I can't answer that part of your question but maybe i can say something about the bullet. The bullet will not be as "deadly", or in physics terms, have as much velocity coming down as it did went going up. The bullet is shot out at thousands of feet per second, and comes down at terminal velocity of about 120 miles per hour. These are crapy units, sorry about that, but I only knew them that way, didnt know off the top of my head in metrics. But anyways, the bullet going up will accelerate negatively (deccelerate) at the same rate as the bullet will accelerate when going down, which is about 9.81 m/s^2.

 

[kuenmao]

A bullet does not accelerate while moving. It only accelerates in the gun barrel, when the gunpowder explodes and pushes the bullet out. Afterwards, it travels at constant velocity.
In air, it slows down because of air resistance, but whatever the case, that has nothing to do with terminal velocity. Terminal velocity refers to the maximum velocity of an object in free fall, falling through a fluid. Since there is no gravity and no air in space, there is nothing about "terminal velocity".
In space, any bullet going any direction for any distance would still be the same as "deadly". In air, but with no gravity, a bullet flying for a further distance would be less deadly, since it would be slowed down by air resistance.

 

[JohnDubYa]

okay, so i have two questions. the first one is, since there is no terminal velocity in a vacuum (this is true, right?), would an object continue to accelerate indefinitely? or is there some other force that would stop the acceleration at some point?

Why would it accelerate at all?

In the absence of air friction, the bullet will hit the ground at the same speed that it leaves the barrel.

In air, the bullet will reach terminal velocity on the way down, striking the ground at a still-deadly speed.

Air resistance, being a velocity-dependent force, breaks the symmetry.

 

[BobG]

Your first question is a little incomplete. I assume you mean that if an object is at some infinite distance from another massive object exerting a gravitational force, the first object continue to acclerate indefinitely (well, at least until the two objects collided). Of course, being so far away at the beginning, the initial acceleration would be infinitely small (almost zero).

If you used values that were more comprehensible, say two objects in space, one twice as far away from the Earth as the other, the one twice as far away will be traveling faster when it hits the Earth than the closer object. When it passes the point the closer object started at, it already has an 'initial' velocity compared to the closer object starting from zero. But it wouldn't be going twice as fast, since its rate of acceleration increases the closer it gets to the Earth.

To the second question, a bullet shot straight up in the air will be traveling at deadly speeds on the way down. There have been rare reports of people being killed when bullets fired in the air in celebration have struck someone on their way down.

Terminal velocity relates to the point when an objects air resistance balances out the acceleration of gravity. For a human body, that happens around 120 miles per hour. I don't know the terminal velocity of a bullet, but it is much more streamlined than a human body and therefore will have a much higher terminal velocity. And while I don't know the number for a bullet's terminal velocity, it has to be high enough to reach deadly speeds or else guns would not be very effective even when fired level. While terminal velocity isn't exactly applicable for a bullet fired level, the effective range and the terminal velocity are affected by same characteristics of the bullet (it's ballistic parameter). If a bullet had a low terminal velocity, then it would also slow down too quickly to be a very effective long range weapon.

 

[AcEY]

hmmm I am actually slightly confused by your second question, when u say the bullet is shot throught the air, do u mean in space cos if u do there is no air, and if u mean air on Earth then then i don't understand the symmetry bit :/

And on the first question, a vacuum is absent of anything (right?) so then it wouldn't leave the barrel at all because there would be nothing for the bullet to replace, i could be wrong :/ come to think of it space is a vacuum isn't it ahh well I am mad ignore me :P

 

[Doc Al]

I agree with what BobG said.

okay, so i have two questions. the first one is, since there is no terminal velocity in a vacuum (this is true, right?), would an object continue to accelerate indefinitely? or is there some other force that would stop the acceleration at some point?

The force that would stop the acceleration due to gravity is that of the Earth smacking into it! But, until the inevitable collision with the ground, in vacuum there would be no terminal velocity.

also, since symmetry dictates that a body that travels upwards through space must take the same amount of time to travel downwards through space (this is also true i think?), then if a bullet were shot straight up in the air, would it be just as deadly on the way back down as on the way up?

That return speed would be the same in a vacuum, but not in air. You may enjoy reading this thread: https://www.physicsforums.com/showthread.php?t=6752

 

[ceres]

There is no such thing as a true vacuum, there is always some molecules bobbing around, something like 12 hydrogen per match box sized area. So the bullet will slow down as fired on Earth just a lot slower.

 

[chroot]

There is such thing as a true vacuum in a model. Many times when modelling real phenomena, physicists must use approximations to simplify calculations. 12 hydrogen atoms per match box volume is not enough to measurably affect the velocity of a bullet, and can safely be approximated by a true vacuum.

- Warren

 

[ceres]

Measurable effect or not, Vacuum is defined as a "space empty of matter" which there clearly isnt.

 

[chroot]

That's irrelevant. We can still talk about true vacuums even if they don't exist.

- Warren

 

[BobG]

That return speed would be the same in a vacuum, but not in air. You may enjoy reading this thread: https://www.physicsforums.com/showthread.php?t=6752

Funny question. I wonder how Oliva and her husband got around to asking that particular question.

The post about the pennies dropped from a tall building reminds me of how Ted Stepien celebrated purchasing the Cleveland Cavaliers around 25 years ago (I don't know why he celebrated that - he was the fourth owner in less than a month - a new NBA record).

Stepien owned the tallest building in Cleveland and a semi-pro softball team. To celebrate buying the Cavaliers, he dropped softballs from the top of his building for one of his softball players to catch. Unfortunately, he failed to account for the wind and the softballs kept blowing into the crowd. One fractured cheek, a fractured wrist, a broken windshield later, the crowd panicked and started fleeing, resulting in numerous other minor injuries.

If there was any bright side, it was that Ted Stepien also owned an insurance company.

Made Sports Illustrated's All-Time Worst Sports Hype list at number two. (Number one also involved falling objects - a boxer that intended to parachute into the ring, but his parachute failed to open - violated the primary rule of advertising - don't kill the main attraction).

 

[JohnDubYa]

There is no such thing as a true vacuum, there is always some molecules bobbing around, something like 12 hydrogen per match box sized area.

What about the space betwen the hydrogen molecules? Hmmmmm?

 

[Nenad]

a vacuum still has forces propagationg through it (gravity), so therefore we cannot have a true vacum. Thats what I think.

 

[Moose352]

Just to point out, if a body is in a vacuum, and there a constant force is exerted on it, it will not accelerate indefinitely even if it doesn't collide with anything. According to special relativity, as the velocity increases the mass of the body also increases, so the acceleration will decrease. Not sure if that helps.

 

[kuenmao]

Just to point out, if a body is in a vacuum, and there a constant force is exerted on it, it will not accelerate indefinitely even if it doesn't collide with anything. According to special relativity, as the velocity increases the mass of the body also increases, so the acceleration will decrease. Not sure if that helps.

We probably won't be dealing with velocities anywhere close to the speed of light, so we can leave special relativity out of this.

a vacuum still has forces propagationg through it (gravity), so therefore we cannot have a true vacum. Thats what I think.

We assumed that it was in space, where the effect of gravity can be neglected because of the great distance.

...And on the first question, a vacuum is absent of anything (right?) so then it wouldn't leave the barrel at all because there would be nothing for the bullet to replace, i could be wrong :/ come to think of it space is a vacuum isn't it ahh well I am mad ignore me :P

You're right that a gun can't be fired, but I don't think it has anything to do with what you're saying. You don't need anything for the bullet to replace. Just think of a spaceship: as long as it has it's engines pushing out liquid hydrogen and oxygen, it doesn't need anything to "replace" to move. However, in the absence of air, a gun can't be fired, because the gunpowder would not explode and it would not push the bullet.
Let's just assume that there is a spring in the gun, so we don't even have to think of the point that a gun can't be fired in the absense of air, shall we?

 

[Rampantbaboon]

the launching of projectiles in space has to do with conservation of momentum. i.e. sending large amounts of molecules out of the back of a spacecraft in order to be sent foreward

 

[etcetera]

A bullet will fire in space. The oxidiser is contained in the gunpowder.

Eric

 

[JohnDubYa]

Mass is a Lorentzian invariant. It does not increase with speed. (There, that should fire everyone up.)

 

[pmb_phy]

We probably won't be dealing with velocities anywhere close to the speed of light, so we can leave special relativity out of this.

Note: This is just an FYI for future reference. Althought this doesn't directly apply to the current thread, at least that I've noticed, I just wanted to point out that just because something is moving slowly it doesn't mean that special relativity doesn't apply. A good example can be found in the article

Relativistic mass increase at slow speeds, Gerald Gabrielse, Am. J. Phys. 63(6), 568 (1995).

Another example is a gas under large pressure. The inertia of the gas (leaving out the container that the gas is in) depends on the pressure of the gas and that pressure can't be ignored when the magnitude of the pressure, p, is comparable in magnitude to the square of the speed of light. Even when the gas is moving very slowly. Notice that p/c² has the same dimensions as mass density. The inertial mass density of the gas, rho, is then

rho = rho₀ + p/c²

So even when v << c, when p ~ c² it effects rho to a signifigant extent. The kinetic energy of the gas is then given by

K = (1/2)rho*V*v² = (1/2)[rho₀ + p/c²]V*v²

Interesting note: The system of gas+container does not depend on pressure. Note also that rho = rho₀ + p/c² only when v != 0. If v = 0 then rho = rho₀.

More examples provided upon request.

Mass is a Lorentzian invariant. It does not increase with speed. (There, that should fire everyone up.)

That's not meaninful until you state what mass you're referring to. Proper mass is an invariant. Relativistic mass does not depend on speed.

However when you say something is not invariant and then you say it does not depend on speed then you're not neccesarily speaking of the same thing.

E.g. let U_pete = Pete's 4-velocity. Let P = 4-momentum of a particle. Then the quantity M_pete defined as the scalar product of U_pete and P divided by c², i.e.

M_pete = P*U_pete/c²

is the relativistic mass of the particle as measured by Pete. Guess what? M_pete is an invariant, and depends on the relative speed of the particle and me, the observer. :-)


Pete