Final speed of particle far away from rings with opposite charges

[risakapal]

Homework Statement

As shown in the figure, a pair of rings of radius R are separated by a distance AR, where A=4, and are aligned with their symmetry axes along the z-axis. The rings have equal but opposite charges. The ring on the left carries charge -q, and the ring on the right carries charge q.

A positively charged particle with charge Q and mass m is released from rest on the z-axis a distance BR, where B = 3 to the right of the midpoint between the charged rings.

Derive an expression for the final speed v of the particle when it is very far away from the ring system in terms of the Coulomb constant k. Keep numerical values exact

Relevant Equations

V = kq/r
U = vq
KE = 1/2mv^2

When I submitted it, this answer was incorrect.

 

[PeroK]

Looks right.

 

[PeroK]

When I submitted it, this answer was incorrect.

It's not a good idea to update a post after someone has replied, as I didn't see this update. You should have added a new post to this thread.

 

[haruspex]

When I submitted it, this answer was incorrect.

Do you know what the official answer is?
Is it checked by software or a person?
The expression could be put in various forms, e.g. $\sqrt{\frac {kQq\sqrt 2}{mR}(1-\frac 1{\sqrt{13}})}$

 

[risakapal]

Do you know what the official answer is?
Is it checked by software or a person?
The expression could be put in various forms, e.g. $\sqrt{\frac {kQq\sqrt 2}{mR}(1-\frac 1{\sqrt{13}})}$

I do not know the official answer. The question is automatically graded. Previously, I have not had issues with the form of the expression, but it may be the case here?

 

[haruspex]

I do not know the official answer. The question is automatically graded. Previously, I have not had issues with the form of the expression, but it may be the case here?

Maybe.
I see the identical question at https://www.chegg.com/homework-help...gned-symmetry-axes-along-axis-rings-q67223093, where it claims it to be solved, but the solution is paywalled.

Anyone have a Chegg account? I'm not hopeful that a) their solution is correct, and b) differs from yours.

 

[PeroK]

I do not know the official answer. The question is automatically graded. Previously, I have not had issues with the form of the expression, but it may be the case here?

I don't see how you could agree on an exact format for an expression like that. For example, there are some people who believe you should never have a square root in a denominator.

 

[Gavran]

The answer $$ v = \sqrt { \frac { k Q q \sqrt { 2 } } { m R } ( 1 - \frac { 1 } { \sqrt { 13 } } ) } $$ is definitely a correct and acceptable answer. But the answer in a form like $$ v = \sqrt { 1,022 \frac { k Q q } { m R } } $$ is not a correct answer because numerical values must be kept exact.

 

[haruspex]

I don't see how you could agree on an exact format for an expression like that. For example, there are some people who believe you should never have a square root in a denominator.

I don't know how smart these systems can be at checking equivalence of algebraic forms.

 

[risakapal]

It worked! I simplified the 1/x^1/2. Thanks for the help.