There’s been a lot of physics in GQ recently, what with “head-on collisions” “knight rider” and the “physics bet”. I’m going to throw in another couple of problems, and invite answers and new riddles. Have fun!
A train proceeds east at 50 mph. A fly proceeds west at 3 mph. After a brief and fatal interaction, both fly and train proceed east at 50 mph.
The fly’s velocity has reversed direction. Since accelerations cannot be instantaneous, at some point in the collision the fly must have been stationary. And since the fly was in contact with the train, the train must also have been stationary.
Did the fly stop the train?
I don’t know the “official” solution to this. I have one of my own, which I’ll post later.
2) Not really a riddle. I stumped my high-school physics teacher (and myself for a while) with this one.
A car accelerates from 0 to 30 mph. Its KE is 900 units (proportional to velocity squared)
The car now accelerates from 30 to 60 mph. Its KE is now 3600 units. So it required an additional 2700 units of energy.
Now, if the car is on the deck of an aircraft carrier which is going at 30 mph, and it accelerates to 30 mph relative to the aircraft carrier (60 mph relative to the Earth) does it require 900 or 2700 units of energy?
If the car only has enough gas to increase its KE by 900 units, does this mean the car can’t reach 30 mph relative to the aircraft carrier?
As for the first one, I’ll give a slipshod answer, but one that makes a point. The fly is never really in contact with the train. Except in extreme conditions, atoms do not actually come in contact with one another.
As for the second one, that’s easy. For the car to accelerate to 30 MPH relative to the aircraft carrier, it only has to expend 900 units’ worth of fuel. However, when it does this, it in fact pushes the carrier backward a little, so that the carrier slows down, so the car isn’t really going 60 MPH relative to the Earth. If the carrier expends 1800 units’ worth of fuel at the same time that the car expends its 900 units, it’ll maintain its 30 MPH. The total amount of fuel used, then, corresponds to 2700 units, which is what you’d expect for the system as a whole. Since you implied that 30 MPH WRT carrier = 60 MPH WRT Earth, we can assume that the carrier does indeed expend 1800 units’ worth of fuel. The answer to your final question is Yes. This, of course, is neglecting air resistance, which is something Physicists love doing anyway.
OK, I’ll take a shot at these. Lets see how bad I can look when the real physics types get to them.
Just because the fly and the train are in contact doesn’t mean the train was ever stopped. It probably did slow down after the collision, but I am not sure any instrument we currently have could detect the velocity change. (We do have to preserve momentum - so the train does need to slow down a tiny bit when it collides with the fly.) The assumptions given in the question are incorrect.
I think that the car only needs the 900 units to get itself moving 30 mph relative to the aircraft carrier. The aircraft carrier, however, will have to expend an extra 1800 units of energy to avoid slowing down in the ocean while the car accelerates. (Those 1800 units would probably be unnoticed in the ongoing expenditure to overcome the drag of the ocean, but I think they would be needed.)
The train does not, at any point during the collision, stop. Think about it this way: If a stationary object were in the tracks, and the train struck this object, would the train stop moving at any point? Of course not (at least, not as long as the object’s mass was less than the train’s). The fly question is basically the same: When the fly hits the train, its (the fly’s) speed drops to zero. At the instant that happens, the problem then becomes one of a massive object pushing a stationary one (since the two are now in contact with one another). The stationary, spattered fly will begin to accelerate in the direction it is being pushed.
So, the answer is, no, the fly did not stop the train.
If you throw a baseball in the air it will travel up until Gravity completely stops its ascent. At the vertex the ball will have a velocity of 0. Since its velocity is 0 and it is just hannging up in the sky for that instant, does gravity stop? Of course not. Too bad though- that would be cool.
Remember there is no absolute velocity, we can only state relitive velocity, The train is moving at 50mph relitive to the ground, 53 mph relative to the fly, basically 0 relitive to the cabose, and probally about mach 25 relitive to the international space station.
upon impact (lets say the fly goes splat on the windshild), the fly’s body starts decelerating at the train/fly interface while it’s butt keeps moving at it’s old speed. As the molecules of the fly start pressurewave in the fly the fly’s velocity starts to take on the trains velocity until the 2 are moving at almost the trains velocity. The train has an identical reaction as a pressure wave flows through the glass and into the frame.
As for your’s 2nd question, the energy required to move a car from 0-30 and then again from 30-60 is because of the wind and rolling resistance, and other internal frictions, but mainly the wind. there was a man called mile-a-minute murphy who many yrs ago rode (50yrs+ est.) a bike at 60mph behind a LIRR car. The ties had wood on them to allow the bike to ride and the train had an enclosed area for him to ride, but was opened at the back incase he fell or couldn’t keep up. he kept up due to aving no air resistance
Everybody got the aircraft carrier and the car right! I remember that being tougher, but then again, I was fourteen…
My take on the train is this - the problem is to accommodate the small time interval in which the fly is accelerated from -3 mph to 50 mph. The fly can’t accelerate instantly, that would imply an infinite force and we just don’t get them in the real world.
During this interval, you have a train moving 50 mph in contact with a fly moving less than 50 mph. Therefore, the small part of the train in contact with the fly MUST be moving less than 50 mph. If you have a monster fly, this leaves you with what is technically known as a “dent.”
with normal flies, the dent is a temporary, local elastic deformation of the paint layer or windshield (K2dave’s pressure wave.) But I contend that for a tiny time interval, a very small part of the train DOES stop. The apparent paradox arises from regarding the train and fly as undeformable objects.
Achernar - an experiment! Find the largest, meanest, ex-special forces combat instructor you can find and punch him (or her) on the nose. Then carefully explain how technically, you never touched him…
There’s no justification for asserting the fly stops. Saying the the fly “stops” is not an invariant statement. It depends on the frame of reference you choose. What if the train was going 52 mph, and the fly only 1? Does it still stop? This is the same situation as the first, but in a reference frame traveling -2 mph. So are you now asserting that part of the train is moving backwards at -2 mph? Isn’t this point in contact with the fly? Why does the fly “win”?
The problem is that the fly doesn’t accelerate as a solid, so the forward-most part of the fly begins accelerating as soon as it starts interacting with the front of the train, so it begins slowing. The part of the train pushing it is in turned being pushed by more of the train behind it. Since the train (even just the engine) is so much more massive than the fly, it can accelerate the fly just by slowing down a little bit.
To determine whether the train stops, you’d have to compare how much compression each of the fly and the train undergo to achieve the same force. Maybe the easiest way to think of this is to imagine the train and fly both have a tiny spring in front. The fly would have to be much less compressible to stop part of the train (producing more force for a given compression). If they were equally compressible, the most you could say is that the touching parts stop in the center of velocity frame, which means a tiny bit of the train slows to 23.5 mph.
I still stand behind my statement that the train never comes in contact with the fly. The electrical repulsion between the electron clouds of the atoms of the train and the atoms of the fly is what accelerates the fly in the opposite direction. When you look at it fundamentally, there are only around four forces, and only a force can accelerate something. Since the train obviously acceleartes the fly, unless you think that the train exerts some sort of gravitational or nuclear force on the fly, this is what has to happen. As counter-intuitive as it is, this is also what happens when a combatant punches me in the face. (I’d have the last laugh, though, if I secretly replace my head with antimatter, and his hand gets annihilated.)
ZenBeam - I agree. You’ve thought this through better than me. Maybe a small diamond will stop a tiny part of the train, but probably not a fly.
Achernar - I wasn’t disagreeing with you! It’s a question of how you want to define “contact.” Personally, I treat everyday electron cloud interactions as “contact” and try and steer clear of nucleus-to-nucleus events, but really I’m not going to argue with someone who has several kilos of antimatter sitting around.
This is just a plainly stupid statement. It’s a sort of “retard elitism” I have always found really irritating. “Look, since all apparent contact is really just electrons replusing other electrons, nothing touches!” Congratulations, moron, that is technically true, but semantically useless. You haven’t disproven contact, you’ve only redefined contact. And your definition gets us nowhere in explaining our fly-locomotive interaction, and is thus stupid.
Nuclear volume, under the same definitions, is as “false” as apparent atomic volume, since protons and neutrons are merely a volume defined by the space taken up by the gluon interactions holding their otherwise volumeless constituent particles. Thus, even your nucleuses don’t really exist, and thus all matter is really not there at all, and I can ignore you, you bumbling idiot, since you don’t really exist at all.
The problem with the OP is that it assumed the fly and train must come fully in contact before the fly starts to get accelerated by the train. “Fully” is the key word here. The fly actually starts to get accelerated when it is partially in contact with the train, at which point the front tip of the fly is travelling at +50mph, and the rear tip at -3mph.
Geez, jaryon32, I’d tell you to get a grip, but since I don’t believe that matter exists:rolleyes:, there would be nothing to get a grip on.
Anyway, I have to disagree with you - my redefintion of contact does in fact explain the paradox. Under the old definition, if two things are in contact, then they’re travelling at the same speed. Under my defnition, when two things are in contact (IE they’re close enough that their electron clouds are significantly interacting) then that’s not necessarily true. Because your mindset encompasses the old defintion, you take the statement from the OP which says “And since the fly was in contact with the train, the train must also have been stationary.” at face value. If you can get around this statement, then it’s not difficult at all to resolve the paradox.
