Perhaps The Prince Should Sort Them Out.
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Conservation of momentum - problem?
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Can't remember the formula, but it does occur to me that, for instance, a bee hitting a train coming in the opposite direction has at some point to change direction as it is carried with the train. if I remember correctly, this would mean that one side of the equation is 'zero', therefore so must the other side. In effect, has the bee stopped the train, even for a fraction of a second? If so, how does anything move anywhere?
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No the train does not stop even for a fraction of a second. It just keeps on rolling. The bee hits the train but neither body is rigid. Assuming the bee hits a metal panel, the surface of the panel will distort slightly, the bee somewhat more. The metal panel will probably spring back into shape, the bee probably will not.
Thanks for this. I see your point but there is still a change in direction. The bee was moving one way then it is moving the other way. This means at some moment in this process it is stopped dead.
Perhaps bees and trains are a confusing analogy. What about two particles colliding? Let's assume two non-identical protons collide, each travelling in the opposite direction. The one with less energy is pushed back along its course by the one with more energy. At some point, the 'weaker' of the two has changed direction.
According to the formula, this renders one side as zero. But even outside the formula, it appears self-evident that in order to change direction, there is a point at which it stops moving one way and begins moving the other way, ie it has stopped. If the weaker has stopped, then the stronger too must have stopped, as it appears impossible to have one body moving and the other stopped dead.
I fear this is a paradox, and one I don't understand. I'd welcome any further thoughts.
Perhaps bees and trains are a confusing analogy. What about two particles colliding? Let's assume two non-identical protons collide, each travelling in the opposite direction. The one with less energy is pushed back along its course by the one with more energy. At some point, the 'weaker' of the two has changed direction.
According to the formula, this renders one side as zero. But even outside the formula, it appears self-evident that in order to change direction, there is a point at which it stops moving one way and begins moving the other way, ie it has stopped. If the weaker has stopped, then the stronger too must have stopped, as it appears impossible to have one body moving and the other stopped dead.
I fear this is a paradox, and one I don't understand. I'd welcome any further thoughts.
Thanks Ice Maiden. I don't want to get off the central point. I was trying to use an analogy where questions of rigidity or significant mass were reduced. I'm not a scientist so perhaps protons are a poor choice. It's the basic idea of a change in direction that is bothering me. As I said, I think this is a paradox (same as the tortoise and hare - which incidentally no-one has yet answered to my full satisfaction).
I presume that it is only the part of the metal (or whatever the bee hit) where the bee hit that had a momentary zero motion, hence a temporary indentation however small. Actually, a bee hitting a train at full speed may indeed leave a permanent dent in a more malleable part of the train such as grill etc.
Google 'bird hits plane' in Images mode and see how much damage a relatively soft animal can do to a metal craft moving at high speed.
Google 'bird hits plane' in Images mode and see how much damage a relatively soft animal can do to a metal craft moving at high speed.
I can see the problem but can't answer it yet. Do you mind if I re-state it?
2 identical particles, same speed, opposite directions. They collide, both stop, then spring apart. Total momentum is zero throughout the collision. That's fine.
One particle is twice the mass of the other. Same speed, opposite directions again. They both change direction therefore they must both be stationary at some time, so their combined momentum will be zero.
There go the laws of physics.
Thinking about it.
2 identical particles, same speed, opposite directions. They collide, both stop, then spring apart. Total momentum is zero throughout the collision. That's fine.
One particle is twice the mass of the other. Same speed, opposite directions again. They both change direction therefore they must both be stationary at some time, so their combined momentum will be zero.
There go the laws of physics.
Thinking about it.
Ok, here goes.
The simple answer is that both particles stop, but they stop at different times. So momentum is conserved. The laws of physics are back.
Here is the morte detailed answer. The 2 particles collide. They distort converting some kinetic energy to potential energy. At the peak of the collision they are both moving at the same speed in the direction of motion of the heavier particle. To do this, the lighter particle has stopped and changed direction. The heavier partice has reduced speed, but not stopped. (As wildwood said, a small part of the heavier particle has momentarily stopped, but most of it kept on going, carrying the momentum.) So far, momentum is conserved. Now the particles spring apart. The heavier particle changes direction, whereas the lighter one just goes faster in the same direction. In the moment the heavier particle is stationary, the lighter particle carries all the momentum.
The simple answer is that both particles stop, but they stop at different times. So momentum is conserved. The laws of physics are back.
Here is the morte detailed answer. The 2 particles collide. They distort converting some kinetic energy to potential energy. At the peak of the collision they are both moving at the same speed in the direction of motion of the heavier particle. To do this, the lighter particle has stopped and changed direction. The heavier partice has reduced speed, but not stopped. (As wildwood said, a small part of the heavier particle has momentarily stopped, but most of it kept on going, carrying the momentum.) So far, momentum is conserved. Now the particles spring apart. The heavier particle changes direction, whereas the lighter one just goes faster in the same direction. In the moment the heavier particle is stationary, the lighter particle carries all the momentum.
two-penneth,
You say in your second post:
"If the weaker has stopped, then the stronger too must have stopped, as it appears impossible to have one body moving and the other stopped dead. "
This is not correct. It IS possible for one body to be moving and the other body to be stopped, but only instantaneously. Think of a black snooker ball you are trying to pot which is stopped. You cue the white ball which moves towards it at some speed, say 15 mph, then just at the moment of contact the white ball is moving at 15mph and the black ball is stopped. A fraction of a second later both balls have accelerated to generally some non-zero velocities.
This is also true if both balls are moving and one of the balls is hit so that it goes back on itself. This ball is at some point stopped but only instantaneously, but the other ball does not stop.
I obviously do not agree with 'etelioni@. It's obvious to everybody that when the poor little bee hits the train that the train does NOT stop! To stop a train moving at say 60mph requires a massive deceleration force and then to get it back up to almost 60mph again, another massive force.
No, the bee stops instantaneously, but the train just keeps going.
You say in your second post:
"If the weaker has stopped, then the stronger too must have stopped, as it appears impossible to have one body moving and the other stopped dead. "
This is not correct. It IS possible for one body to be moving and the other body to be stopped, but only instantaneously. Think of a black snooker ball you are trying to pot which is stopped. You cue the white ball which moves towards it at some speed, say 15 mph, then just at the moment of contact the white ball is moving at 15mph and the black ball is stopped. A fraction of a second later both balls have accelerated to generally some non-zero velocities.
This is also true if both balls are moving and one of the balls is hit so that it goes back on itself. This ball is at some point stopped but only instantaneously, but the other ball does not stop.
I obviously do not agree with 'etelioni@. It's obvious to everybody that when the poor little bee hits the train that the train does NOT stop! To stop a train moving at say 60mph requires a massive deceleration force and then to get it back up to almost 60mph again, another massive force.
No, the bee stops instantaneously, but the train just keeps going.
Sorry eltelioni, I didn't read your posts carefully enough! I agree with what you are saying. Please accept my apologies.
My post is just to address the misconception of the original poster. He/she seems to think that if one body stops, then the other body must also stop, but this is clearly not true if only one body reverses direction.
My post is just to address the misconception of the original poster. He/she seems to think that if one body stops, then the other body must also stop, but this is clearly not true if only one body reverses direction.
I'm puzzled by the assertion that "According to the formula, this renders one side as zero. "
I'm no scientist but I thought conservation of momentum meant the combined momentum was unchanged
Suppose big object had mass of 10 kg and velocity of 10m/s, and little object had mass of 1 kg and velocity of -10 m/s (as it's going in opposite direction). Total momentum (in whatever the units would be) is 100-10=90
After collision if there is a point at which the little object has zero velocity, if momentum is conserved the bigger object
must slow down slightly (to 9 m/s?) but is certainly still moving.
The train doesn't stop!
I'm no scientist but I thought conservation of momentum meant the combined momentum was unchanged
Suppose big object had mass of 10 kg and velocity of 10m/s, and little object had mass of 1 kg and velocity of -10 m/s (as it's going in opposite direction). Total momentum (in whatever the units would be) is 100-10=90
After collision if there is a point at which the little object has zero velocity, if momentum is conserved the bigger object
must slow down slightly (to 9 m/s?) but is certainly still moving.
The train doesn't stop!
Hi Vascop- yes, my comments were directed at two-penneth. Your postings have dealt with this query now.
I assume that two-penneth is referring to Zeno's tortoise and hare paradox in which it an be argued the hare never catches the tortoise http://www.bbc.co.uk/dna/h2g2/A541937
I assume that two-penneth is referring to Zeno's tortoise and hare paradox in which it an be argued the hare never catches the tortoise http://www.bbc.co.uk/dna/h2g2/A541937
Hi guys and thanks for your input. You see my problem arises when we use words like 'instantaneously' and 'fraction of a second'. This may well be relevant for considering what Factor30 correctly identifies re the tortoise and the hare paradox (thanks for the link, I'll take a look).
I also thought the formula of which i write had velocity at its heart.
I'm no Deep Thought as is self evident but I need to go away and think about it. Cheers again.
I also thought the formula of which i write had velocity at its heart.
I'm no Deep Thought as is self evident but I need to go away and think about it. Cheers again.
I think your problem is not actually related to bees and trains. The fact that one or the other may happen to deform is irrelevant.
We can just switch examples.
I think your problem comes about in the way you are idealising the problem.
You are considering a split fraction of a second - in effect "freezing" time.
But then you are considering quantities such as momentum and velocity which relate to the rate of change in position.
If I show you a picture of a car and ask you how fast it is moving you cannot say - I have "frozen" time - you need to observe it in time to tell.
Similarly when you observe a collision - you cannot say anything about the momenta from a single time slice which is what you are trying to do when you talk about an increasingly short fraction of a second.
Essentially in this circumstance, concepts like velocity and momentum cease to have meaning.
Take any two fractions of a second however and you can talk about velocities and momenta again and the all the numbers will balance.
Sorry to seem a little evasive but I hope if you think about it you'll see that the question doesn't actually have meaning.
We can just switch examples.
I think your problem comes about in the way you are idealising the problem.
You are considering a split fraction of a second - in effect "freezing" time.
But then you are considering quantities such as momentum and velocity which relate to the rate of change in position.
If I show you a picture of a car and ask you how fast it is moving you cannot say - I have "frozen" time - you need to observe it in time to tell.
Similarly when you observe a collision - you cannot say anything about the momenta from a single time slice which is what you are trying to do when you talk about an increasingly short fraction of a second.
Essentially in this circumstance, concepts like velocity and momentum cease to have meaning.
Take any two fractions of a second however and you can talk about velocities and momenta again and the all the numbers will balance.
Sorry to seem a little evasive but I hope if you think about it you'll see that the question doesn't actually have meaning.
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