Capacitor and Mechanics question, IPhO 2004

[Mantaray]

Homework Statement

It's theoretical question 1 d) I'm having problems with, I'm at a loss as to where I have gone wrong with my approach? The question has been attached.

Homework Equations

see attachment please

The Attempt at a Solution

see attachment please.

It's quite a lengthy problem I suppose, so a hearty thanks to whoever takes the time to take a look!

 

[hikaru1221]

1/ The threshold voltage is wrong. Hint: the E-field that exerts force on the disk is not V/d. Here we also need to reason a bit
2/ Have you tried computing it to the final answer? Let me rewrite your final equation as:
$v_s^2(1-\eta ^2)(1+\eta ^2)=2d\eta ^2(\eta ^2a_1+a_2)$
Oops, what happened to $\eta ^4$? Where is it?

 

[Mantaray]

1/ The threshold voltage is indeed wrong, I was thinking that the lower plate would exert a force upwards on the disc, but it does not since there is no electric field under the small plate. Therefore only the field of the upper plate exerts a force on the disc.

2/ I'll be thinking about that for some longer... I maybe should've taken into account the velocities instead of the plain speed, or does it work out? The solutions should be somewhere on the web too, but that would be cheating.

 

[Mantaray]

Hmm I was able to work your formula out to the final answer provided in the solution manual, but I lost a factor two in my accelerations. I used the force exerted on the disc by the electric field, which is $\chi$$V^{2}$/(2dm). Then if I input $a_{1}$ = $\chi$$V^{2}$/(2dm) - g and $a_{2}$ = -$\chi$$V^{2}$/(2dm) -g, I'm a factor two short in $\chi V^{2}/m$ in the final answer. Or have I just made another mistake in my algebra?

 

[hikaru1221]

Maybe I would be more helpful if I can see your full work Sorry, I'm lazy
Anyway, I guess there should be something wrong with the algebra.