1
$\begingroup$

Writing an (maths) exam question for 'ordinary' level engineers, examining vectors, I had written a question along the lines of "a slinky of mass 1 kg goes down a flight of stairs... the top of the stairs is at $A$ while the bottom is at $B$... find the work done by the gravity force $-9.81\,\mathbf{k}$ in pulling it down the stairs..."

Then I thought maybe I could spice it up by a little by having a spiral staircase and I would basically have the same question...

However then I realised there was no centripetal force that would keep the slinky in circular motion...

The only thing I could posit --- and wouldn't put on the exam --- was that the slinky might be ferromagnetic and the central pole might be a magnet...

Is it theoretically possible for a ferromagnetic slinky to travel down a "magnetic" spiral staircase analogously to how it goes down a 'linear' staircase.

I believe it is but I couldn't convince myself (in particular my recall of the properties of the magnetic field isn't great).

$\endgroup$
2
$\begingroup$

The problem you will quickly run into is the fact that the force depends on the gradient of the magnetic field, and the magnetization depends on the strength of the field.

This means that any "reasonable" arrangement of magnets (which will have to be attractive, from the center of the spiral) will give you an unstable equilibrium. As soon as the slinky gets too close, it will be pulled to the center; get a little too far, and your slinky will escape.

The only way I could see this work would be if you had a diamagnetic slinky (that is, it gets repelled by a magnetic field), and the magnets were on the outside of the spiral. Now, as the slinky gets close to the outside it gets repelled more strongly, and you have a stable situation.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.