Object Falls in Vacuum at the acceleration due to gravity.

[x G r E e D]

Lets say there was a vacuum cylendar straight off of the Earth that reached far past the son, let's just say it went an infinite distance away. So if I drop an object let's say a pen in the vacuum going towards the Earth and it was falling at the acceleration due to gravity. (9.8m/s2) And if there is no terminal velocity in a vacuum shouldn't the pen keep accelerating? So if it keeps accelerating then could the pen reach the speed of light?

If I drop a pen in an infinite length vacuum that had the gravitational pull of the Earth, will the pen reach the speed of light?

 

[DavidSnider]

The acceleration due to gravity is only 9.8m/s^2 on the surface of the earth. As you get farther away the effect of gravity is much less.

 

[sophiecentaur]

But remember, g is only 9.81m/s/s on the Earth's surface. The inverse square law applies and, as you go further away, the acceleration decreases and decreases. At a 'great distance', the acceleration would be nearly zero!
But that is a mere detail. Whatever the force on your pen, the limit to the speed achieved (relative to any attracting mass, however large) must be less than c. This can be thought of as being due to the effective mass of the pen getting bigger as it gets faster, due to relativistic effects.

The actual speed achieved will be limited to the difference in gravitational potential energy at the starting distance and the potential at the Earth's surface. That is all the energy that would be available to transfer into Kinetic energy and is no way infinite!

 

[hyfpbvr]

General equation for gravity force F = (G m1*m2)/r*rso if you have a infinity r you will have a infinity small gravitational force

 

[Lsos]

The further you go from the earth, the less that Earth's gravity accelerates you. Also, as Earth's gravity pulls you in, you're moving faster and faster and closer and closer to the earth, and as the faster you go, the less time that gravity has to keep accelerating you before you finally hit the damn thing (the earth). So, there very much is a finite velocity that the pen will accelerate to. In fact, this velocity is pretty well known, and can be easily calculated.

The fastest possible speed that something can be accelerated to from rest by Earth's gravity is 11.2 km/sec. This is called "escape velocity", and it's also the speed that you need to throw something at for it to be able to escape the pull of the Earth and keep going to an infinite distance. Anything less, and the object will either fall back to earth, or go into some sort of orbit around it.

For the moon, escape velocity is 2.4 km/s
For Jupiter, it's 59.5 km/s
For the sun, it's 617.5 km/s

Interestingly, there are objects in the universe which actually have an escape velocity GREATER than the speed of light. So, yeah, not even light can escape the pull of their gravity. And if you fall in, you're supposed to get accelerated to beyond the speed of light. Of course, this is impossible and so it's probably why our laws of physics break down inside these objects. I'm sure you can figure out by now what these objects are called...

 

[ideasrule]

=
Interestingly, there are objects in the universe which actually have an escape velocity GREATER than the speed of light. So, yeah, not even light can escape the pull of their gravity. And if you fall in, you're supposed to get accelerated to beyond the speed of light. Of course, this is impossible and so it's probably why our laws of physics break down inside these objects. I'm sure you can figure out by now what these objects are called...

Our laws of physics don't break down inside these objects, unless you're talking about Newton's laws; in fact, it was general relativity that predicted the existence of these objects in the first place. It's also not true that light can't escape them because of their escape velocity. It's more accurate to think of them as curving space so much within their event horizons that all possible wordlines--that is, all possible paths that an object can take--have the center in their future.

 

[HallsofIvy]

The object accelerates at a smaller and smaller rate until it reaches the center of the earth. After that it decelerates assuming it doesn't hit the side of the cylinder (which, due to the rotation of the Earth means you have to drill from north pole to south pole), and that there is no resistance whatever, the object would take the same time, and same distance to decelerate as it had to accelerate. That means that it would be back to 0 velocity at the moment it reached the other side of the earth- and then it would fall back again.

Assuming no friction at all, it would oscillate from one side of the Earth to the other.

 

[sophiecentaur]

Lsos
yes, of course, it's escape velocity! I was thinking the other way round and didn't make the lateral step like you did.

Hallsovivy
The restoring force in the 'hole' is proportional to the distance from the centre ( in classical situations) so you have simple harmonic motion. The period is independent of amplitude of oscillation.

 

[Lsos]

Our laws of physics don't break down inside these objects, unless you're talking about Newton's laws; in fact, it was general relativity that predicted the existence of these objects in the first place. It's also not true that light can't escape them because of their escape velocity. It's more accurate to think of them as curving space so much within their event horizons that all possible wordlines--that is, all possible paths that an object can take--have the center in their future.

You can explain why light can't escape this thing in quite a few different ways, and not one needs to be exclusively the "correct" reason. Since escape velocity actually has something to do with what the OP was asking about, that's why I brought it up. No need to shoot me down and start throwing space-time curvatures in my face

And, we have laws that describe how really small things behave and how really large, gravitationally powerful things behave. But we have no laws for both...which is exactly what the object I'm talking about is.

We just don't know what the hell happens in there.

 

[sophiecentaur]

This a typical example of two agendas going on at once. There's the 'obvious' classical problem and then there's the advanced Physics approach. I wonder whether we should have a system of 'stars' or equivalent, for questions, so that contributors can tell at what level the original question is aimed.
I always feel sorry for a questioner who just wants the simple 'schoolboy' response and who then gets both barrels of Relativity and Quantum explanations. There is no limit to the number of levels of possible response and there will always be someone who can give it the very highest level of treatment and totally gobsmack the OP.
Dunno what the real solution is to that one - if we want to be helpful for every contributor.