# Momentum and energy in a collision

1. Aug 13, 2013

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?

2. Aug 13, 2013

### Staff: Mentor

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?

3. Aug 13, 2013

4. Aug 13, 2013

### Staff: Mentor

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

5. Aug 13, 2013

:d ok

6. Aug 14, 2013

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 lets 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 text books 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 amout of distance - energies become equal and text books 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???? :)

7. Aug 14, 2013

### Staff: Mentor

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.

8. Aug 14, 2013

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

9. Aug 14, 2013

### Staff: Mentor

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

10. Aug 14, 2013

### 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.

11. Aug 14, 2013

### sophiecentaur

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.

12. Aug 15, 2013

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...

13. Aug 15, 2013

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 dont grow on trees or lay on the ground...it's more like a law on a paper.

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

Last edited: Aug 15, 2013
14. Aug 15, 2013

### sophiecentaur

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.

15. Aug 15, 2013

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>???????????

16. Aug 15, 2013

### Staff: Mentor

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.

17. Aug 15, 2013

### sophiecentaur

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.

18. Aug 15, 2013

### Staff: Mentor

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.

19. Aug 15, 2013

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

20. Aug 15, 2013

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 lets 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 text books 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 amout of distance - energies become equal and text books 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???? :)

21. Aug 15, 2013

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 text books.

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?

Last edited: Aug 15, 2013
22. Aug 15, 2013

### Staff: Mentor

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.

23. Aug 15, 2013

### sophiecentaur

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! :tongue2:

24. Aug 15, 2013

Why, momentum is "created" from force multiplied by time, lets 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... ;)

25. Aug 15, 2013

Right.