Capacitor and Mechanics question, IPhO 2004

In summary, the conversation discusses a theoretical question involving the wrong threshold voltage and calculations for the final answer. The conversation also mentions factors and equations that may have been missed or calculated incorrectly. The solution manual is mentioned as a possible resource, but cheating is discouraged.
  • #1
Mantaray
17
0

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!
 

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  • #2
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 :smile:
2/ Have you tried computing it to the final answer? Let me rewrite your final equation as:
[itex]v_s^2(1-\eta ^2)(1+\eta ^2)=2d\eta ^2(\eta ^2a_1+a_2)[/itex]
Oops, what happened to [itex]\eta ^4[/itex]? Where is it? :biggrin:
 
  • #3
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.
 
  • #4
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 [itex]\chi[/itex][itex]V^{2}[/itex]/(2dm). Then if I input [itex]a_{1}[/itex] = [itex]\chi[/itex][itex]V^{2}[/itex]/(2dm) - g and [itex]a_{2}[/itex] = -[itex]\chi[/itex][itex]V^{2}[/itex]/(2dm) -g, I'm a factor two short in [itex]\chi V^{2}/m[/itex] in the final answer. Or have I just made another mistake in my algebra?
 
  • #5
Maybe I would be more helpful if I can see your full work :smile: Sorry, I'm lazy :biggrin:
Anyway, I guess there should be something wrong with the algebra.
 

Related to Capacitor and Mechanics question, IPhO 2004

1. What is a capacitor?

A capacitor is an electronic component that stores electrical energy in the form of an electric field. It consists of two conductive plates separated by an insulating material, known as a dielectric.

2. How does a capacitor work?

When a voltage is applied to a capacitor, one plate becomes positively charged and the other becomes negatively charged. This creates an electric field between the plates, which stores the electrical energy. The capacitor then discharges this energy when connected to a circuit, providing a temporary source of power.

3. What is the unit of capacitance?

The unit of capacitance is farad (F). It is defined as the amount of charge required to create a potential difference of one volt between the plates of a capacitor.

4. How do capacitors differ from batteries?

Capacitors and batteries both store electrical energy, but they differ in their storage mechanisms. Batteries use chemical reactions to store energy, while capacitors use an electric field. Capacitors also have the ability to discharge energy quickly, while batteries release energy over a longer period of time.

5. How are capacitors used in electronic circuits?

Capacitors have a wide range of applications in electronic circuits. They can be used to filter out noise, stabilize power supply voltages, store energy for timing circuits, and act as a temporary power source in case of power interruptions. They are also commonly used in audio and radio frequency circuits.

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