What Equations Calculate Force and Energy in a Gauss Gun Setup?

[Exadoi]

Hi guys I am new, have tried to look for a topic similar to this and have some stuff vaguely relating to the topic but most is due to solenoids and 'dipoles' ?

Ok, for a Physcis EEI i am trying to find the most beneficial arrangement of magnets and ball bearings for a Gauss gun that magnifies the velocity of the first ball bearing xfering to the last ball bearing in the series. I have done my testing on an aluminium track, where i recorded how far each ball bearing rose up a curve so i could calculate energy from E=Mgh, simple enough. But i have realized i must also calculate the theoretical value so i can compare it with my practical value.

I am using solid neodymium magnets of 5300 gauss or .53 telsa (ithink) that are cylindrical 0.01m*0.01m and was wondering what equation i could use to work out the force acted upon the first ball bearing (0.01m radius, 0.00351kg) in the series, which was given no extra velocity by me, only the velocity that the magnetic field acted upon it ( this ball bearing is attracted by the magnet when 0.02m away from it).


I also would appreciate it if someone could explain how i could give/find the Potential Energy Difference of the first ball bearing (which would be at 0m due to its close proximity to the magnet) and the Potential Energy of the last Ball bearing in the system which changes from a displacement of 0.02m - 0.04m from the magnet (in the sereis of test due to a differnt number of 'buffer ballbearings). With the Kinetic energy gained from the 0.02m of acceleration of the first ball bearing (by the magnet) i could then subtract from it the Magnetic Potential Energy of the ball bearing to be launched to discover the total energy impacted onto the last ball bearing in the series (and do this for Displacements of 0.02,0.03 & 0.04m)

*If there is no way to calculate the first part concerning the velocity of the ball bearing, i may simply time how long it takes for the ball bearing to reach the magnet and use SUVAT to calculate the velocity* however the Magnetic potential energy part is still eluding my knowledge of physics and is my greatest priority. However if an equation or series of equations exists for the frist part, it would be helpful as it would be introduce a lesser degree of error than using SUVAT

Any suggestion/advice would be greatly appreciated

I apologise for the length of the question, but i wanted to explain myself clearly and i hope that i have used correct abbreviations for my values etc (i have attempted to explain them clearly also)

I hope this is not classed as a 'Homework Question" and if deemed so i will move it to the other forum, as i am not asking for somebody to give me the answer but show me what tools to use so i may calculate them myself (i have only included the values to give a genearl idea of my experiment).

 

[eljose79]

Hi, welcome to the forum! It sounds like you have a really interesting topic for your EEI. The use of magnets and ball bearings in a Gauss gun is definitely related to solenoids and dipoles, as you mentioned. The key principle at play here is electromagnetic induction, which is the production of an electromotive force (EMF) in a circuit by a changing magnetic field.

To answer your first question about calculating the force acting on the first ball bearing, you can use the equation F = BIl, where F is the force, B is the magnetic field strength, I is the current (or in this case, the velocity of the ball bearing), and l is the length of the conductor (in this case, the length of the track). Since you know the values for B and l, you can solve for the force acting on the ball bearing.

For the second part of your question about potential energy, you can use the equation PE = mgh, where PE is potential energy, m is the mass of the ball bearing, g is the acceleration due to gravity, and h is the height. In this case, h would be the displacement of the ball bearing from the magnet. You can calculate the potential energy at different displacements and compare them to determine the change in potential energy.

I hope this helps you with your calculations. Good luck with your EEI! If you have any further questions, don't hesitate to ask.