Non-constant acceleration

[Tleilaxu]

I was experimenting with electromagnets and I noted how a neutral steel ball being attracted to one end of the cylindrical electromagnet had an increasing acceleration. Because, as the distance between the steel ball and the electromagnet decreased, the force attracting it increased; thus increasing the acceleration. Now, assuming the electromagnet is held in place, I was curious as to how I could work out the velocity of the steel ball just before it hits the electromagnet when placed and released at certain distances from the electromagnet. And also when rolled towards the electromagnet at a steady velocity (assuming no friction). I am quite sure you would have to use definite integrals but I am not sure at to how you would work this out.

 

[jpm]

For me the hard part would be working out the relationship of force vs distance. If you solve that, then it is relatively easy to integrate to get energy and equate to kinetic energy in the ball... do not forget that the ball is rotating and energy goes into making it rotate. Another possibly minor problem is that changing flux pattern will induce voltages in the coil, altering mmf. My brain is starting to hurt...

 

[israelkk]

You ahve to solve the "magnetic circuit" of the complete electromagnet with ball/plunger in a numerical analysis fashion. I did it and wrote a computer simulation to analyse high speed DC on-off electro-pneumatic valves. This is the only way to calculate the valve time response. I also calulated the impact speed to be able to check the orifices sealed by the plumger. However in the valve analysis you also have to take into account the fluid pressure and sealing pressure which complicates the modeling.