Cracking the Physics Olympiad Problem: Expressing V in 5 Parameters

[olympiad]

hey, I have a tough time cracking this one
The other problem is:
Imagine a glass tube with steel rings around it which have a conductancy rho and a half diameter of R. they are spaced with a distance H.
inside the glass tube is a much smaller glass tube. Through it you drop a magnet with mass m and magnetic moment mu. the magnet will reach a final speed V quite soon. Explain with which factor the endspeed V will change if in five different experiments the five parameters(H,R,rho,M,mu) are doubled. You can neglect all form of friction, selfinduction and reciprocal induction.

I have a partial answer. You have to express v in the five parameters and then it is easy. If the speed is constant all height energy over a height H will be transferred into electric energy, so MHg=Pt with P the electric power and t the time that it takes to fall down a length of H. that time t is V/H. P is I^2*R.
So MHg=(V/H)*R*I^2. the problem is, how do you express I? mu=a*m^2 so I thought that the solution would be I=mu/(pi*R^2). (magnetic moment divided by area of one ring) But that can't be true because other rings have influence too, and now I just calculate the influence of one ring. Also, I don't take into account the distance between the rings. If you express V in this way H isn't in the formula, that can't be right. Help me please? thank you in advance.
olympiad

 

[Nate810]

level questions are hard. The way to solve this problem is to use the equation of motion. Since there is no friction or self-induction, the only force acting on the magnet is the Lorentz force due to its interaction with the rings. The equation of motion is F = ma, so the acceleration of the magnet is given by F/m. We then need to calculate the Lorentz force. This can be done using the Biot-Savart law, which states that the magnetic field B at a point P due to a current element I is given by B = (mu_0I)/(4*pi*r^2) where r is the distance from the current element to P. We can integrate this over all the current elements in the rings to get the total Lorentz force. Now that we have the equation of motion, we can find the final speed V. We can then use this to calculate how V changes when the five parameters are doubled. The answer should be that V is doubled in each experiment.

 

[M98Ranger]

Hi there,

I understand that you are struggling with this physics olympiad problem and have been working on finding a solution. It seems like you have made some progress in expressing V in terms of the five parameters, but you are still unsure about the accuracy of your solution. I would suggest taking a step back and reviewing the problem again to make sure you fully understand what is being asked.

One approach you can take is to break down the problem into smaller parts and tackle them one at a time. For example, you can start by considering the effect of doubling each parameter individually and see how it affects the final speed V. This can give you some insight into how each parameter contributes to the overall result.

Additionally, you can try using some basic principles and equations from electromagnetism to help you in your solution. For example, you can use Faraday's law to relate the change in magnetic flux to the induced electromotive force (EMF) in the loop of wire. This can help you express V in terms of the magnetic moment mu and the area of the loop.

It's also important to keep in mind the assumptions made in the problem, such as neglecting friction and self/induction. Make sure you are not including them in your solution as they may lead to incorrect results.

I hope this helps and good luck with your solution! Remember to take your time and approach the problem systematically. With some persistence and critical thinking, I am sure you will be able to crack it. Best of luck!