Physics behind Gaussian Accelerator/ Magnetic Linear Accelerator

[x85247x]

Hi all. i have seen some videos on youtube and i am amazed by the videos of Gaussian accelerator/ Magnetic linear accelerator. As i have a physics project coming up i may consider using this for my project, however i need to ensure that this experiment is within my syllabus. i have basically seen explanations from comments by other people in youtube and i realized there are many different type of explanations from people. Some explanations are * Newton 2nd and 3rd law*, *Conservation of energy, conservation of momentum* and something related to the * Newton's cradle* Base on people explanation, i did check them up on Wikipedia but i can't really seem to understand or confirm my understanding. Thus i hope people here can provide assistance such as provide me with explanation for this experiment.
If there is one, include the laws in explanation.

Below are some Videos that i have watched related to Gaussian accelerator/ Magnetic linear accelerator. （Not mine)

http://www.youtube.com/watch?v=i6JCzkSAc5E&feature=related
http://www.youtube.com/watch?v=epf1AUvG32M&feature=related


All helps are appreciated!

 

[Bob S]

This is a nice little science project, but it certainly is not original. Basically a ball bearing is attracted to a strong neodymium-iron magnet, and the momentum at impact is mechanically transferred through the magnet to an equal mass ball bearing on the other side of the magnet that is only weakly attracted to (slowed down by) (restraining force) the magnet due to the two extra ball bearings that act as spacers. So it acts like a momentum multiplier.

 

[x85247x]

Thanks Bob, but does it include any law in it? Anyone?

 

[Bob S]

Thanks Bob, but does it include any law in it? Anyone?

Assume the impulse (momentum integrated over time) from the first ball bearing (BB) is transferred to the second BB with 100% efficiency. This would be true, only if the two BBs have the same mass. If the magnetic force of attraction of the first BB is less than the magnetic force of attraction of the second (true because of the two stationary BBs after magnet), the accelerated BB will have a higher momentum than the first, let's say 20% higher (guess)(1.20 = impulse or momentum multiplier). Then with ten impulse multipliers in a row, the momentum after the last will be 1.20^10 = 6.19 times the first. If this were true, then if the first BB rolled down a 10 cm high slope, then the last one would have 6.19 times the velocity of the first, or 38.34 times as much energy, and should roll up a 383 cm high hill (E = mgh). What we are not completely accounting for is what is the efficiency of the rotational energy transfer. The moment of inertia of a BB is 0.4mR^2 where R is radius, so the total kinetic energy of a rolling BB is 0.5 mv^2 (linear) plus 0.2mv^2 (rotational) = 0.7 mv^2. So there are probably different efficiencies for transferring the linear momentum and the rotational momentum. Your project should explain why the impulse (momentum) is multiplied, and not the energy. Your project should try to measure the rolling momentum transfer multiplier. You should also do the experiment on a greased track so that all the BBs slide instead of roll, and determine the momentum transfer multiplier for sliding BBs.

 

[x85247x]

Assume the impulse (momentum integrated over time) from the first ball bearing (BB) is transferred to the second BB with 100% efficiency. This would be true, only if the two BBs have the same mass. If the magnetic force of attraction of the first BB is less than the magnetic force of attraction of the second (true because of the two stationary BBs after magnet), the accelerated BB will have a higher momentum than the first, let's say 20% higher (guess)(1.20 = impulse or momentum multiplier). Then with ten impulse multipliers in a row, the momentum after the last will be 1.20^10 = 6.19 times the first. If this were true, then if the first BB rolled down a 10 cm high slope, then the last one would have 6.19 times the velocity of the first, or 38.34 times as much energy, and should roll up a 383 cm high hill (E = mgh). What we are not completely accounting for is what is the efficiency of the rotational energy transfer. The moment of inertia of a BB is 0.4mR^2 where R is radius, so the total kinetic energy of a rolling BB is 0.5 mv^2 (linear) plus 0.2mv^2 (rotational) = 0.7 mv^2. So there are probably different efficiencies for transferring the linear momentum and the rotational momentum. Your project should explain why the impulse (momentum) is multiplied, and not the energy. Your project should try to measure the rolling momentum transfer multiplier. You should also do the experiment on a greased track so that all the BBs slide instead of roll, and determine the momentum transfer multiplier for sliding BBs.

Thanks a lot BoB!

 

[Vinny_R]

Bob and x85247x,
The physics behind a Gauss Rifle more commonly known as a Magnetic Linear accelerator are a bit more subtle than those described by Newton. Although the magnet does indeed attract the steel ball to it, thereby increasing the velocity of the initial ball which, after the collision, lends to a higher velocity of the fired ball. However if one were to solve the equations of motion, and note the "potential energy" "stored" in the magnetic field one would realize that the velocity of the fired steel ball should only be on the order of 1.25 times that of the initial steel ball, however we know this is not the case as we see in the experiments the velocity of the fired ball is many times that of the initial ball.
The question is where does this extra velocity come from?
The steel ball is a ferrite material which naturally has dipole moments occurring. One can think of the orientation of the dipoles, with respect to the magnetic field ,as stored potential energy. The initial ball has randomized dipole moments, (ie potential energy), as the ball gets closer to the magnetic field the dipoles start to naturally align releasing the potential energy, so in essence when the initial steel ball touches the magnet all the dipoles align with the magnetic field releasing their stored up potential energy.
What's cool about this is because the dipole orientations have natural preferred states with a probability of H/KbT (where H is some constant, Kb is Boltzmann's constant, and T is absolute temperature) through experimentation you should be able to verify that initial hot slow moving balls will produce faster moving fired balls, than cold balls initial balls moving at the same speed. This is because as the temperature of the ball increases the dipole moments within the ball become more randomized, i.e. the stored potential energy increases.
For a more in depth discussion on this I recommend Griffith's intro text on Electromagnetic Theory found here; https://www.amazon.com/dp/013805326X/?tag=pfamazon01-20 or for those more well versed in this topic check of David Jackson's EMT text.

 

[Bob S]

Try doing this experiment with only one steel ball (the recoil ball) on the downstream side of the neodymium magnet and see if the accelerator works. It won't. Now try it with 2 or 3 steel balls on the downstream side. Why does it work with 2 or 3 balls, and not with one? It is because the magnetic binding energy of the second or third ball on the downstream side of the magnet is less than the binding energy of the incident ball on the upstream side of the magnet. Does it depend on the "natural preferred" dipole moment of the incident ball? Probably not.
Bob S

 

[Per Oni]

Try doing this experiment with only one steel ball (the recoil ball) on the downstream side of the neodymium magnet and see if the accelerator works. It won't. Now try it with 2 or 3 steel balls on the downstream side. Why does it work with 2 or 3 balls, and not with one? It is because the magnetic binding energy of the second or third ball on the downstream side of the magnet is less than the binding energy of the incident ball on the upstream side of the magnet. Does it depend on the "natural preferred" dipole moment of the incident ball? Probably not.
Bob S

I do agree with this post.
In fact the magnets being used are powerful but small which means that most of the energy is very close to the magnet. The incident ball touching receives far more magnetic energy then the projectile loses.
I don’t see how dipole moment comes into it but I could be wrong.

 

[Bob S]

I don’t see how dipole moment comes into it but I could be wrong.

Per Oni-
I agree.
Bob S

 

[soc3393]

Assume the impulse (momentum integrated over time) from the first ball bearing (BB) is transferred to the second BB with 100% efficiency. This would be true, only if the two BBs have the same mass. If the magnetic force of attraction of the first BB is less than the magnetic force of attraction of the second (true because of the two stationary BBs after magnet), the accelerated BB will have a higher momentum than the first, let's say 20% higher (guess)(1.20 = impulse or momentum multiplier). Then with ten impulse multipliers in a row, the momentum after the last will be 1.20^10 = 6.19 times the first. If this were true, then if the first BB rolled down a 10 cm high slope, then the last one would have 6.19 times the velocity of the first, or 38.34 times as much energy, and should roll up a 383 cm high hill (E = mgh). What we are not completely accounting for is what is the efficiency of the rotational energy transfer. The moment of inertia of a BB is 0.4mR^2 where R is radius, so the total kinetic energy of a rolling BB is 0.5 mv^2 (linear) plus 0.2mv^2 (rotational) = 0.7 mv^2. So there are probably different efficiencies for transferring the linear momentum and the rotational momentum. Your project should explain why the impulse (momentum) is multiplied, and not the energy. Your project should try to measure the rolling momentum transfer multiplier. You should also do the experiment on a greased track so that all the BBs slide instead of roll, and determine the momentum transfer multiplier for sliding BBs.

Hello Bob, can you please explain why and how

a) "Assume the impulse (momentum integrated over time) from the first ball bearing (BB) is transferred to the second BB with 100% efficiency. This would be true, only if the two BBs have the same mass"

b) "The moment of inertia of a BB is 0.4mR^2 where R is radius, so the total kinetic energy of a rolling BB is 0.5 mv^2 (linear) plus 0.2mv^2 (rotational) = 0.7 mv^2." Here can you explain why 0.4mR^2 becomes 0.2mv^2 (rotational)?

 

[diermas]

Bob and x85247x,
The physics behind a Gauss Rifle more commonly known as a Magnetic Linear accelerator are a bit more subtle than those described by Newton. Although the magnet does indeed attract the steel ball to it, thereby increasing the velocity of the initial ball which, after the collision, lends to a higher velocity of the fired ball. However if one were to solve the equations of motion, and note the "potential energy" "stored" in the magnetic field one would realize that the velocity of the fired steel ball should only be on the order of 1.25 times that of the initial steel ball, however we know this is not the case as we see in the experiments the velocity of the fired ball is many times that of the initial ball.
The question is where does this extra velocity come from?
The steel ball is a ferrite material which naturally has dipole moments occurring. One can think of the orientation of the dipoles, with respect to the magnetic field ,as stored potential energy. The initial ball has randomized dipole moments, (ie potential energy), as the ball gets closer to the magnetic field the dipoles start to naturally align releasing the potential energy, so in essence when the initial steel ball touches the magnet all the dipoles align with the magnetic field releasing their stored up potential energy.
What's cool about this is because the dipole orientations have natural preferred states with a probability of H/KbT (where H is some constant, Kb is Boltzmann's constant, and T is absolute temperature) through experimentation you should be able to verify that initial hot slow moving balls will produce faster moving fired balls, than cold balls initial balls moving at the same speed. This is because as the temperature of the ball increases the dipole moments within the ball become more randomized, i.e. the stored potential energy increases.
For a more in depth discussion on this I recommend Griffith's intro text on Electromagnetic Theory found here; https://www.amazon.com/dp/013805326X/?tag=pfamazon01-20 or for those more well versed in this topic check of David Jackson's EMT text.

At what temperatures will this start to actually affect the ball? I did up to 100 degrees C (using basic school equipment) with no change in how much the balls were accelerated (varying from 10x as fast to almost 40).