Physics? Anyone that can solve the mistery?

[Deleted]

Heya!
2 days ago, while gulping beers like madmen, me and a friend had a dispute.
We've seen a movie about an ipad being dropped from 30 km. The problem was not in the realization of the "drop", but - one of us said that it'd be the same if the ipad was dropped from 30 km or 3 km, the other one said that the dropped object would increase its speed the longer it fell. We were ranting about terminal velocity, and whether that falling object, were it given enough drop distance, would gain infinite speed or not.
Anyone that has any idea about physics that could enlighten us?
Thanks in advance!

[Cuno]

Honestly, I think http://en.wikipedia.org/wiki/Terminal_velocity sums it up pretty nicely.

As the object accelerates (usually downwards due to gravity), the drag force acting on the object increases, causing the acceleration to decrease. At a particular speed, the drag force produced will equal the object's weight (mg). At this point the object ceases to accelerate altogether and continues falling at a constant speed called terminal velocity (also called settling velocity). An object moving downward with greater than terminal velocity (for example because it was thrown downwards or it fell from a thinner part of the atmosphere or it changed shape) will slow down until it reaches terminal velocity.

[Deleted]

It would reach terminal velocity. Eventually the force pushing up on it (air resistance) would equal 9.81N and then the force would be constant on the object and it would maintain a constant velocity and trajectory.

[Marimba]

Heya!
2 days ago, while gulping beers like madmen, me and a friend had a dispute.
We've seen a movie about an ipad being dropped from 30 km. The problem was not in the realization of the "drop", but - one of us said that it'd be the same if the ipad was dropped from 30 km or 3 km, the other one said that the dropped object would increase its speed the longer it fell. We were ranting about terminal velocity, and whether that falling object, were it given enough drop distance, would gain infinite speed or not.
Anyone that has any idea about physics that could enlighten us?
Thanks in advance!

No, it wouldn't, due to terminal velocity as a result of wind resistance. In a vacuum however it would keep accelerating until it hit something.

[Deleted]

We hit that bottleneck as well - were that object to fall in a hypothetical vacuum that spanned indefinetely - would the object reach light speed and surpass it?
The simpler question - would an object falling from 3 km have the same impact speed as one falling from 30km?

[zakayron]

well basically if you have no start velocity just dropping it from a given height then:
-9.8x^2+h
where h is your drop height would give you your position at any given time
Take the derivative of that and you get -19.6x is your velocity after a given time x.
However obviously you will meet wind resistance so the velocity is capped in earth's atmosphere.
If you wanted to simulate an ipad dropping in a vacuum being accelerated by gravity eventually you would reach relativistic speeds however there is a universal speed limit at the speed of light so no it would not reach an infinite speed.

The preceding post may or may not have been a large rambling but it should answer your question

[Pfeff]

No, it wouldn't, due to terminal velocity as a result of wind resistance. In a vacuum however it would keep accelerating until it hit something.

No it wouldn't

[Deleted]

No, it wouldn't, due to terminal velocity as a result of wind resistance. In a vacuum however it would keep accelerating until it hit something.

Technically true, but not the whole truth. It'd keep accelerating a slower and slower rate as it approached the speed of light (which is the fastest known speed that a Boson can travel at (As we all know, certain Mesons could possibly travel faster)) and it would converge to a limit of 0.00...repeat to infinity...1 below light speed.

---------- Post added 2012-01-17 at 11:44 PM ----------

We hit that bottleneck as well - were that object to fall in a hypothetical vacuum that spanned indefinetely - would the object reach light speed and surpass it?
The simpler question - would an object falling from 3 km have the same impact speed as one falling from 30km?

First one, no. Second one, depends on the object.

---------- Post added 2012-01-17 at 11:44 PM ----------

No it wouldn't

Actually it would. Sort of.

[zakayron]

We hit that bottleneck as well - were that object to fall in a hypothetical vacuum that spanned indefinetely - would the object reach light speed and surpass it?
The simpler question - would an object falling from 3 km have the same impact speed as one falling from 30km?

No.
No in a vacuum unless you have retarded amounts of attraction.

[Deleted]

No in a vacuum unless you have retarded amounts of attraction.

Any less than infinite attraction would yield slightly different impact speeds. Infinite anything is impossible. Therefore no. :P

[haxartus]

(As we all know, certain Mesons have been found to travel faster)

I'm not so sure about that.
They arrive faster. It's a completely different thing. If the results are even correct.

[Mormolyce]

We hit that bottleneck as well - were that object to fall in a hypothetical vacuum that spanned indefinetely - would the object reach light speed and surpass it?
The simpler question - would an object falling from 3 km have the same impact speed as one falling from 30km?

An object in a vacuum subjected to a constant acceleration will accelerate indefinitely however it will approach the speed of light asymptotically, ie approach it but never actually reach it. To put it another way, as the velocity gets closer to the speed of light the acceleration decreases but never actually reaches zero.*

As for the object falling 3km or 30km it depends on how far it has to fall before reaching terminal velocity. Terminal velocity is determined by the equilibrium between the force of gravity pulling it down versus the resistance of the air pushing back up. The faster you go the stronger the air resistance and eventually they balance out - the acceleration stops and the object falls at a constant speed. A very aerodynamic object will experience less drag (air resistance) than a non-aerodynamic one, basically you're looking at shape and surface area. So depending on what you're dropping it may or may not have reached terminal velocity by 3km (probably would've though).

*(All of this of course depends on your frame of reference but let's not get overly technical ^_^)

[Badpaladin]

Remember, air is not a vacuum -- it's a ton(literally speaking a lot more than a ton, punlol) of particles. The faster you move through those particles, the more particles you have to move through at a given time.

[Deleted]

I'm not so sure about that.
They arrive faster. It's a completely different thing. If the results are even correct.

Fair point. I'll ammend my post.

[Laize]

We hit that bottleneck as well - were that object to fall in a hypothetical vacuum that spanned indefinetely - would the object reach light speed and surpass it?
The simpler question - would an object falling from 3 km have the same impact speed as one falling from 30km?

Nothing can reach the speed of light.

As something accelerates, it becomes more massive. This requires more and more force to accelerate it faster and faster. Only an infinite force given infinite time could move a particle to the speed of light.

Fun fact, "speed of light" is not just a speed unique to light, but to spacetime. 3x10^8 m/s is also the speed of gravity, the speed of electromagnetic fields (duh) and the speed at which any massless particle will move.

[Linkedblade]

I don't even think "infinite speed" is something that legitimately exists.

The speed of light is finite. Nothing can surpass the speed of light. Therefore an object could not have "infinite speed."

Even if an object could travel at infinite speed classic physics wouldn't be able to describe this motion. To mathematically show this would be silly. This object (considering Earth's acceleration due to gravity) would be accelerating at 9.8 m/s^2. velocity = acceleration*time. So solving for how long this object would take to accelerate to infinite speed would take and infinite amount of time. ^_^

∞ m/s = 9.8 m/s^2 * t
[∞ m/s]/[9.8 m/s^2] = t
∞ s = t

[mojo6912]

The air is more dense the closer you get to the ground. So if it reaches terminal velocity before it hits the ground, wouldn't it start to actually slow down?!

[rkma]

Even in a vacuum, an object would never accelerate faster than the speed of light relative to the object that it is gravitationally attracted to. However, it will still continue to accelerate until it hits the object, and may even appear to be accelerating at a constant rate to certain observers.

[saangreal]

ww w.telegraph.co.uk/science/science-news/8901001/Speed-of-light-broken-again-as-scientists-test-neutrino-result.html#disqus_thread

[haxartus]

ww w.telegraph.co.uk/science/science-news/8901001/Speed-of-light-broken-again-as-scientists-test-neutrino-result.html#disqus_thread

There are a few possibilities that they might travel at normal speed but still arrive earlier.