Energy and conservation of momentum confusion

In summary, the conversation discusses the relationship between force and kinetic energy in the scenario of a bullet firing from a gun. It is determined by the masses of the two objects and the conservation of momentum. The kinetic energy of the bullet is greater due to the squared factor in the equation. The chemical energy in the explosive is converted into kinetic energy when the gun is fired.
  • #1
Jimmy87
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If you consider a bullet firing from a gun then you have conservation of momentum and a Newton's third law pair (according to what i have read on the internet anyway). They both experience the same force if they are a third law pair but, generally, what is it that determines which object receives more energy? For instance, the bullet has a huge kinetic energy after the gun has fired whereas the gun has very little. So where does energy conservation fit into this example and what is the relationship between energy and force (if there is one)? They are both receiving the same force yet experience different energies?
 
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  • #2
The relationship between kinetic energy and force is the work energy theorem. It states that ##\frac{1}{2}mv^{2}(x) - \frac{1}{2}mv^{2}(x_0) = \int _{x_0}^{x}F(x')dx'##.
 
  • #3
Jimmy87 said:
So where does energy conservation fit into this example and what is the relationship between energy and force (if there is one)?
It doesn't.
The kinetic energy is not conserved in this process.
It is like the reverse of a plastic (non-elastic) collision.
The initial KE is zero, the final KE is not.

The distribution of KE is determined by the masses of the two objects.
And maybe the external factors.
 
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  • #4
WannabeNewton said:
The relationship between kinetic energy and force is the work energy theorem. It states that ##\frac{1}{2}mv^{2}(x) - \frac{1}{2}mv^{2}(x_0) = \int _{x_0}^{x}F(x')dx'##.
This is of no help in this problem!
You are correct to realize that the bullet and the gun are a "Newtons 3rd law pair"
However conservation of energy is not enough to sort out the details, conservation of energy requires consideration of all the energies involved in the interaction.
 
  • #5
technician said:
This is of no help in this problem!
You are correct to realize that the bullet and the gun are a "Newtons 3rd law pair"
However conservation of energy is not enough to sort out the details, conservation of energy requires consideration of all the energies involved in the interaction.
What are you even talking about? He asked for a relationship between force and kinetic energy. The work energy theorem doesn't require conservation of energy to hold. The determination of the final velocities of the two objects involved in the process only requires conservation of momentum and by itself illuminates why the significantly more massive object doesn't have a recoil velocity comparable to the exit velocity of the smaller mass; he asked for something extra.
 
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  • #6
Jimmy87 said:
For instance, the bullet has a huge kinetic energy after the gun has fired whereas the gun has very little.
Are you sure about this? It is not obvious.
The bullet has a high speed and the gun has a much smaller recoil speed.
But the mass of the bullet is much smaller than that of the gun.
Their kinetic energies my be quite similar.
 
  • #7
Jimmy, you are right, an equal force acts on both. Both the bullet and the gun will receive equal momentum (mv), so if you know the masses of each and the velocity after firing of one, you can work out the velocity of the other. You can then calculate the kinetic energy (mv^2)/2 of each. You will find that the kinetic energy of the bullet is greater because of the squared factor.

When the gun fires, chemical energy in the exposive is converted to kinetic energy.
 
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  • #8
Jimmy87 said:
If you consider a bullet firing from a gun then you have conservation of momentum and a Newton's third law pair (according to what i have read on the internet anyway). They both experience the same force if they are a third law pair but, generally, what is it that determines which object receives more energy? For instance, the bullet has a huge kinetic energy after the gun has fired whereas the gun has very little.
Yes.

M = gun's mass; V = gun's velocity after shot
m = bullet's mass; v = bullet's velocity after shot

momentum conservation:

MV + mv = 0 → v = -(M/m) V

from here you see that |v| > |V|.

Now let's see kinetic energy T:

Tgun = 1/2 M V2
Tbullet = 1/2 m v2 = 1/2 m (-M/m)2 V2 = 1/2 (M2/m) V2

Tbullet/Tgun = M/m.

So, for example, if m = 20g and M = 5kg, Tbullet is 250 times Tgun.
 
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  • #9
Wow that's a lot of very useful information, thanks to all!
 

What is the difference between energy and conservation of momentum?

Energy is the ability to do work, while conservation of momentum is the principle that states the total momentum of a closed system remains constant over time.

Why is conservation of momentum important in understanding energy?

Conservation of momentum is important because it helps us understand how energy is transferred and conserved in different systems, such as collisions or explosions.

How are energy and momentum related?

Energy and momentum are related through the concept of work. Work is the product of force and displacement, and since momentum is equal to mass times velocity, work can also be expressed as force times velocity. This shows that changes in momentum are closely related to changes in energy.

Can energy be lost or gained in a system without a change in momentum?

Yes, energy can be lost or gained in a system without a change in momentum. This is because energy and momentum are not always directly proportional, and there are other factors at play such as friction or external forces.

How does conservation of momentum apply to real-world situations?

Conservation of momentum applies to many real-world situations, such as car crashes, rocket launches, and billiard balls colliding. It helps us understand and predict the outcomes of these events and is an important principle in physics and engineering.

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