I am literally 5 compared physicists-a tire rolls down hill and it keeps rolling faster can it increase in speed infinitely as long as the hill is infinitely large?
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In a vacuum? Possibly. Not in a vacuum no it’ll hit terminal velocity at some point. Do to air friction , water friction , and friction with the hill and possibly other forces it will have to max out eventually. In a vacuum with no air or water it would most likely speed up close to infinite I suppose
No, a tire would not be able to accelerate infinitely. Even in a vacuum, the sheer centrifugal force would pull the tire apart.
In classical physics, yes.
BUT, under relativity, the closer the ball gets to the speed of light, the more energy it needs to “push” it the same amount.
So it would essentially get closer and closer to the speed of light.
*this is assuming we ignore wind resistance, and the fact that the tire would tear itself apart well before anything relativistic starts to take effect.*
As it approaches the speed of light, it would take an ever-increasing amount of force to pull it faster. No physical object can reach the speed of light, and nothing including light can exceed it. So could it *increase* in speed forever? Yes but the rate it accelerates will slow so it inches ever closer to the speed of light but never reaches it.
In the real world the “speed limit” would be terminal velocity where air resistance is slowing it as much as gravity is speeding it up. The behavior is the same, it will slowly approach this speed limit but won’t pass it.
Setting aside relativistic limitations (the increasing amount of energy it takes to accelerate mass as it reaches the speed of light), you cannot place an object at an “infinite” height atop an infinite hill.
It doesn’t make sense in a real physical sense to say two objects are infinitely far apart. Two physical items cannot be literally infinitely far apart. As long as you’re talking about two real objects that exist somewhere in space, there is a finite amount of space separating them.
if the tire is rolling freely and not being propelled, then rolling is going to be slower than falling because it will get slowed down because it touches the road. Air still provides some slowing (like when a cold wind blows and you feel it on your cheek) but far less than the road would, even a steep one.
If you kept making the hill steeper and steeper, making the tire go faster and faster; eventually it would be straight up and down and the tire would only be falling like if you dropped it from an airplane.
Because the air slows a falling thing down just a little bit, there is a limit to how fast a tire can fall to the ground. That speed is the limit of how fast it could possibly roll down a hill, but probably not quite that fast because of the road slowing.
This is an interesting problem because it forces us to examine our assumptions.
We have two possible interpretations of the infinitely long hill, for example – is gravity constant or not? (I suppose you could even argue for a 3rd where the hill itself had mass so as you went down the direction of gravity would change).
Connected to that we have the vexed question of air resistance – do we assume none, a constant air pressure or does air pressure increase as we descend the hill?
We know that there is friction between the tyre and the ground, because the tyre is stated to be rolling (rather than sliding) and the rate of roll is increasing.
My answer would be that the tyre would increase in speed until air resistance balanced out the forces. Remove air resistance, and there is a race between the tyre flinging itself apart from centrifugal forces and something odd happening at the interface where rubber meets ground, causing the tyre to stop accelerating the spin and move to a constant spin speed but sliding across the ground too, so the speed of the tyre doesn’t match the speed across the ground. This would also cause the tyre to disintegrate quickly. Assuming though that you can make the tyre indestructible in some way, what you have is essentially a magic gravity powered particle accelerator. I’m pretty sure that there would be some gotcha that makes the tyre subject to the normal issues with approaching lightspeed (steadily increasing mass means the acceleration reduces so you asymptotically approach lightspeed), but my currently horribly sleep deprived brain is refusing to come up with a reason that makes sense in a magic universal gravity field, as the mass of the accelerated object cancels in those equations. In the most extreme case, where something in the magic allows that continuous acceleration at a constant rate, the mass of the tyre would quickly increase to the point where it became a black hole itself, taking us into exotic physics country where you’d have to work out how the magic gravity field interacted with the singularity. *Something* must stop it accelerating at a constant rate or it’ll quickly become an object with a mass-energy high enough that we have no reference outside the big bang itself.
It’s my understanding that, even in a vacuum, an object can’t fall faster than the planets escape velocity. Rolling resistance from contact with hill aside, escape velocity of the earth is 11.2 km/s. So that’s as fast as it could roll under ideal hypothetical conditions.
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