Momentum and energy in a collision

[ataskaita]

Lets say an archer shoots an arrow or a gun fires a bullet, why is it that a lighter objects (arrow and a bullet) gain larger kinetic energy than the heavier one's? Shouldn't it be Newtons 3rd law: force from the gun powder at the equal distance hence same gained kinetic energy?

 

[mfb]

At least to me, it is not clear which processes you compare.
Do you compare an arrow shot by a bow with a bullet shot by a gun? They have completely different acceleration mechanisms, it should not be surprising that the kinetic energy is different.
Something else?

 

[ataskaita]

At least to me, it is not clear which processes you compare.
Do you compare an arrow shot by a bow with a bullet shot by a gun? They have completely different acceleration mechanisms, it should not be surprising that the kinetic energy is different.
Something else?

Um, hate that i asked, because i think i already know the answer, is it possible to delete the Thread?

 

[Dale]

It is possible, but once you get a response we usually don't.

 

[ataskaita]

It is possible, but once you get a response we usually don't.

:d ok

 

[ataskaita]

Hmm, well i thought I figured it out, but then I got another idea. The way i sort of figured it out was that if a bullet is shoot out of pistol, so by the Newtons 3 law recoil and a force on a bullet are equal and if we think that a time let's say it takes to fire is 1 second and a force is 10 N, then 10/10kg *1 sec (10kg - mass of a gun) - we get 1 m/s and the bullet of 1 kg 10/1kg * 1 sec is 10 m/s kinet energy would be 5 and 50 J. The confusion in the first place was that i thought if forces should be equal in opposite directions then energy should be equal, but textbooks tell us that we should use momentum to calculate this and with that energy is absorbed more by lighter object... I got the numbers ok, like in this example when i used equal amount of time - 1second. But then if we use equal amount of distance - energies become equal and textbooks say that it is wrong that energies are equal, because ligther objects absorb more energy out of overall energy "packet"... So why is it that a "trick" with time works and a trick with distance doesn't? :)

 

[mfb]

But then if we use equal amount of distance

The bullet moves more than the gun (this is a result of momentum conservation), you don't have equal distances. If you assume something wrong, you get a wrong result - not so surprising.
Bullet and gun interact with each other for the same duration - they have to, as an interaction always involves both parts.

 

[ataskaita]

result of momentum conservation

Ok, but that's math... is there a way to visualize it to explain it in a "real world form"?

 

[mfb]

The same interaction time between bullet and gun might be a more intuitive explanation.

 

[robphy]

Play... http://phet.colorado.edu/en/simulation/collision-lab (the momenta diagram is important)


Collisions [that is, interactions] between two particles exchange momentum [impulse]... essentially Newton III. (Total Momentum conservation is NOT math... it's fundamental physics.)

Conservation of total energy holds... provided you properly account for ALL of the forms of energy in the interaction. Nothing can be left out. Inelastic collisions (or their time-reversal "an explosion of a single object") do not conserve total mechanical energy.


The real "trick" is to start from the fundamental laws of physics, then draw logical conclusions from it as applied to that problem. As a check of what you assume, ask yourself and prove to yourself why your particular starting point is true.

 

[sophiecentaur]

Ok, but that's math... is there a way to visualize it to explain it in a "real world form"?

You are discounting Maths as not being relevant. In fact, it's a language which states relationships and allows the drawing of valid conclusions because it is possible to manipulate equations in a much more reliable way than just waving your arms and talking in vague "real world" terms. When people decide that Maths is not for them, they are cutting themselves off from a huge amount of Physics and Engineering. There is just no access to some topics without the help of Maths.

 

[ataskaita]

You are discounting Maths as not being relevant. In fact, it's a language which states relationships and allows the drawing of valid conclusions because it is possible to manipulate equations in a much more reliable way than just waving your arms and talking in vague "real world" terms. When people decide that Maths is not for them, they are cutting themselves off from a huge amount of Physics and Engineering. There is just no access to some topics without the help of Maths.

Yea, but you can't draw conclusions from math if things are new to you... math is just a rule... and to use the rule you first have to know the basis and the reason for that rule... i.e. direction of angular velocity vector - it's nonsense it doesn't have a physical meaning...

 

[ataskaita]

Play... http://phet.colorado.edu/en/simulation/collision-lab (the momenta diagram is important)Collisions [that is, interactions] between two particles exchange momentum [impulse]... essentially Newton III. (Total Momentum conservation is NOT math... it's fundamental physics.)

Conservation of total energy holds... provided you properly account for ALL of the forms of energy in the interaction. Nothing can be left out. Inelastic collisions (or their time-reversal "an explosion of a single object") do not conserve total mechanical energy. The real "trick" is to start from the fundamental laws of physics, then draw logical conclusions from it as applied to that problem. As a check of what you assume, ask yourself and prove to yourself why your particular starting point is true.

You can draw logical conclusions only if you know that you have accounted for all the variables, that's one thing and another is to know how the variables interact...and only then you can draw a conclusion... for example it is strange to me that let's say MIT course OCW 8.01 about angular momentum...a guy (teacher) says that there is no angular momentum because the is no sin or cos don't remember of theta... i would just say that there is no angle hence no momentum, because angular momentum is angular because of an angle... the same is with maths you can't explain maths with math, because math is based on real world not the other way around (i believe so, because "our" maths is not perfect) plus math don't grow on trees or lay on the ground...it's more like a law on a paper.

The same interaction time between bullet and gun might be a more intuitive explanation.

Ok, but why not a distance?

P.S. when i try to use my intuition it almost always fail... of course i know why, it's because it is made unintuitive on purpose... no one wants to give his knowledge for free

 

[sophiecentaur]

Yea, but you can't draw conclusions from math if things are new to you... math is just a rule... and to use the rule you first have to know the basis and the reason for that rule... i.e. direction of angular velocity vector - it's nonsense it doesn't have a physical meaning...

I agree that it is essential that the starting point for the use of Maths in a Science question must be with a valid model but, particularly when you are dealing with a well established bit of Science, you can use the results with confidence. If the sums tell you that you get a certain vector in such a direction then you will get that vector and you've solved the problem.
How can you be anything like sure that your non-maths based conclusions have even a chance of being correct? Science is a rule-based discipline and rejecting Maths as a way into it is just shooting yourself in the foot. It shows common patterns in all sorts of circumstances and, as such, it gives you a way into new topics. OK, you don't like Maths. But you need to get over that problem and start to treat Maths as a tool and an aid. Why do you think it is so universally used? It's certainly not because it's easy - it has to be because it works. If you find it too difficult then you may have to accept (as we all do at some point) that a particular door is closed to you and you just have to 'accept' certain things without a 'good' understanding.
Examine your use of Maths in more familiar circumstances - like your finances, for instance. Would you rather accept the result of a compound interest calculation on a loan or would you just believe a salesman who tells you that you can afford it? In that instance, you are familiar with the Maths and will use it without question. (I should hope).

You have ot bear in mind that Science never really took off until they used Maths.

 

[ataskaita]

I agree that it is essential that the starting point for the use of Maths in a Science question must be with a valid model but, particularly when you are dealing with a well established bit of Science, you can use the results with confidence. If the sums tell you that you get a certain vector in such a direction then you will get that vector and you've solved the problem.
How can you be anything like sure that your non-maths based conclusions have even a chance of being correct? Science is a rule-based discipline and rejecting Maths as a way into it is just shooting yourself in the foot. It shows common patterns in all sorts of circumstances and, as such, it gives you a way into new topics. OK, you don't like Maths. But you need to get over that problem and start to treat Maths as a tool and an aid. Why do you think it is so universally used? It's certainly not because it's easy - it has to be because it works. If you find it too difficult then you may have to accept (as we all do at some point) that a particular door is closed to you and you just have to 'accept' certain things without a 'good' understanding.
Examine your use of Maths in more familiar circumstances - like your finances, for instance. Would you rather accept the result of a compound interest calculation on a loan or would you just believe a salesman who tells you that you can afford it? In that instance, you are familiar with the Maths and will use it without question. (I should hope).

You have ot bear in mind that Science never really took off until they used Maths.

I agree only with one thing that people say - that good things are simple and good doesn't mean a good guy who just created Linux for free I mean good means powerful and strong.. plus i don't reject math I just hate it :D Yet so how about that distance and duration>??

 

[mfb]

Ok, but why not a distance?

There is no reason why the distance should be the same.
If you throw an apple, the apple moves ~1m before it leaves your hand. Do you move backwards 1m at the same time? The same applies to the gun and the bullet.

 

[sophiecentaur]

I agree only with one thing that people say - that good things are simple and good doesn't mean a good guy who just created Linux for free I mean good means powerful and strong.. plus i don't reject math I just hate it :D Yet so how about that distance and duration>??

You just need to learn to love it - a bit at a time.

Can you re-state that question on its own please? I warn you that the answer may (need to) contain Maths.

 

[Dale]

Conservation of momentum is not math, it is physics. Of course, being physics, it can be written mathematically, but it is physics in and of itself. You cannot learn physics if you avoid conservation principles.

Regarding energy, both momentum and energy are always conserved, but in this scenario there is more than just mechanical energy involved. So the conservation of momentum is more useful for analyzing the kinematics.

 

[ataskaita]

There is no reason why the distance should be the same.
If you throw an apple, the apple moves ~1m before it leaves your hand. Do you move backwards 1m at the same time? The same applies to the gun and the bullet.

No it's not the end position it's the interaction... with momentum and wrongly with energy still the distance after the interaction (the throw) wouldn't be equal... masses differ

 

[ataskaita]

You just need to learn to love it - a bit at a time.

Can you re-state that question on its own please? I warn you that the answer may (need to) contain Maths.

I copy paste it:

Hmm, well i thought I figured it out, but then I got another idea. The way i sort of figured it out was that if a bullet is shoot out of pistol, so by the Newtons 3 law recoil and a force on a bullet are equal and if we think that a time let's say it takes to fire is 1 second and a force is 10 N, then 10/10kg *1 sec (10kg - mass of a gun) - we get 1 m/s and the bullet of 1 kg 10/1kg * 1 sec is 10 m/s kinet energy would be 5 and 50 J. The confusion in the first place was that i thought if forces should be equal in opposite directions then energy should be equal, but textbooks tell us that we should use momentum to calculate this and with that energy is absorbed more by lighter object... I got the numbers ok, like in this example when i used equal amount of time - 1second. But then if we use equal amount of distance - energies become equal and textbooks say that it is wrong that energies are equal, because ligther objects absorb more energy out of overall energy "packet"... So why is it that a "trick" with time works and a trick with distance doesn't? :)

 

[ataskaita]

I've got another brilliant idea- we should model elastic interactions with rubber balls and not billiard that way we could see the interaction, but how to model a gun and a bullet -with a spring of course.I believe that's an answer to my own question. And i must point out that momentum and all other explanations suck, including in i believe almost all physics textbooks.

But then comes the more difficult part, what if a guns interaction with a bullet is instant- then what? how can you model it? there is no time, no distance it is just instant and of course you can't even call it an instant event, because there is no time and distance :D It's more like before and after and in such case dt (as in dv/dt) fails. Or there might just be no instant interactions and all collisions would be like rubber balls... who knows? Maybe you know?

 

[Dale]

momentum and all other explanations suck

What an infantile response.

But then if we use equal amount of distance - energies become equal

Why would you use equal distances? The distances are not equal.

A bullet is pushed by expanding gas. Because the gas is expanding the distance the gas pushes the bullet is much longer than the distance the gas pushes the gun.

 

[sophiecentaur]

But then if we use equal amount of distance

When you throw a stone, how far back does your body move and how far forward does the stone move whilst it's in your hand? The distances are Not the same. The work done on the stone is the Force times a large distance (that turns into the stone's KE) and the work done on you is the same force times very little distance at all (you are stuck to the ground) , which means you get no KE (or, at least, very little). However, if you consider the Momentum, the change in momentum is force times time. The same force and the same time for both you and the stone so you both gain equal and opposite momentum (net momentum is zero). And you can't do that without some Maths - I snuck it in there in words but it's still there!

 

[ataskaita]

What an infantile response.

Why would you use equal distances? The distances are not equal.

A bullet is pushed by expanding gas. Because the gas is expanding the distance the gas pushes the bullet is much longer than the distance the gas pushes the gun.

Why, momentum is "created" from force multiplied by time, let's use not time, let's use distance - then what would we get? The idea why would we create artificial quantity momentum by using time and not distance?

It's not so simple if you think that bullet stays stationary and and the gun is pushed... ;)

 

[mfb]

Or there might just be no instant interactions and all collisions would be like rubber balls...

Right.

 

[voko]

Why, momentum is "created" from force multiplied by time, let's use not time, let's use distance - then what would we get?

Then you would get work, which is energy.

The idea why would we create artificial quantity momentum by using time and not distance?

And why would one be more artificial than the other?

 

[ataskaita]

Right.

If that is right, are there indivisible particles in nature and if they collide what happens? They stick? Because if they are not like rubber balls then they can't compress or maybe they just disappear and not stick to each other?

 

[ataskaita]

Then you would get work, which is energy.
And why would one be more artificial than the other?

Maybe because momentum doesn't incorporate distance into it... and if we think that distance does exist how can it be that two particles colliding bring with them their momentum, shouldn't they bring energy with them instead? Energy does include distance. It's like using momentum and adding two cars with three wheels each and getting the right answer - 2 cars, but the number of wheels would be wrong 3+3=6, because in reality in that case it is 4+4=8 and momentum doesn't care about wheels it only cares about cars (momentum could even think that there are no wheels 0+0=0). I hope you get what i mean. Of course momentum does have a distance in it, which is part of speed, but then energy has that distance squared... and how would we get that square from unsquared distance in a momentum, because i sort of think that when you add two things together - you should think about all their parts, well at least in physics.

Edited: not also, but instead (shouldn't they bring energy with them instead)

 

[voko]

Maybe because momentum doesn't incorporate distance into it...

You may want to know that these days distance and time are interchangeable, any distance can be converted into time by dividing it with the speed of light, and any time can converted into distance by multiplying it with the speed of light.

In fact, the unit "meter" is defined as whatever distance is traveled by light in a particular fraction of one second, so distance is in a way secondary to time.

and if we think that distance does exist how can it be that two particles colliding bring with them their momentum, shouldn't they bring energy with them also?

They certainly do. Momentum and energy are two different aspects of motion. Special relativity unites them just like it unites space and time.

It's like adding two cars with three wheels each and getting the right answer - 2 cars, but the number of wheels would be wrong - 3+3=6, because in reality in that case it is 4+4=8 and momentum doesn't care about wheels it only cares about about cars. I hope you get what i mean.

Sorry, I could not make any sense out of that.

Of course momentum does have a distance in it, which is part of speed, but then energy has that distance squared... and how would we get that square from ansquared distance in a momentum

By squaring the magnitude of momentum?

 

[ataskaita]

You may want to know that these days distance and time are interchangeable, any distance can be converted into time by dividing it with the speed of light, and any time can converted into distance by multiplying it with the speed of light.

In fact, the unit "meter" is defined as whatever distance is traveled by light in a particular fraction of one second, so distance is in a way secondary to time.
They certainly do. Momentum and energy are two different aspects of motion. Special relativity unites them just like it unites space and time.
Sorry, I could not make any sense out of that.
By squaring the magnitude of momentum?

If you square the magnitude of momentum you do not get energy unless maybe you use that momentum-energy relation, in that case it is kinda funny to teach momentum in school if you need special relativity to get it. Plus square is a very things changing stuff if you square something - you really produce BIG change on it.

And if you couldn't get any sense of that writing of mine, well again - momentum doesn't care about the 4 wheels of a car, momentum only thinks that it is one or two or three cars, but not the number of their wheels, but energy does care...