Can an alternative approach to using hints solve this electric dipole question?

[SpartanG345]

Homework Statement

This is a mastering physics question but it does not count for my assessment mark, i am using an alternative approach to the one given in the hints. And off course i got the question wrong but i don't understand why..

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Consider an electric dipole located in a region with an electric field of magnitude E ointing in the positive y direction.The positive and negative ends of the dipole have charges +q and -q respectively, and the two charges are a distance D apart The dipole has moment of inertia I about its center of mass. The dipole is released from angle Theta and is allowed to rotate freely

Homework Equations

Equation for torque
Angular acceleration formula given I(moment of inertia and Torque)

The Attempt at a Solution

Let A = angular acceleration
Let T = Theta

I said that dA = (qEdSin(T))/T
then I integrated that to get A in terms T and then i integrated the question again.
Wouldn't the integration of A get the equation of the angular velocity equation?
Obviously you can see where the maximum velocity i use the initial angle and the final angle( when it is lined with the y axis) to find the maximum velocity
can this approach work?
I have never been that good at calculus... would the integration of A between 0 and x give the final velocity at x?
Is this approach wrong?

By the way mastering physics suggested to use conservation of energy
Thank you in advance

 

[tiny-tim]

Hi SpartanG345!

(have an alpha: α and a theta: θ and a tau: τ and an omega: ω )

Consider an electric dipole located in a region with an electric field of magnitude E ointing in the positive y direction.The positive and negative ends of the dipole have charges +q and -q respectively, and the two charges are a distance D apart The dipole has moment of inertia I about its center of mass. The dipole is released from angle Theta and is allowed to rotate freely
…
I said that dA = (qEdSin(T))/T
…
By the way mastering physics suggested to use conservation of energy

(did you mean dA = (qEdSin(T))/I ? or did you mean dω = (qEdSin(T))/I ? )

No.

τ = dL/dt = I dω/dt

you seem to have written τ = I dα, whatever that means.

Try again.

(better still, use work done = E.displacement = increase in KE)

 

[SpartanG345]

whoops i meant dA = (qEdSin(T))/I
where A is the angular acceleration
I think this is right or do I need a dτ in that equation
where T is the angle theta

I was meant to say τ = Iα

But to get a function of α in need to integrate a differential equation as the force changes with θ
where α = T/I, but i am not really sure how to construct this differential equation for a dθ

I was planing to integrate A to get the velocity
ps thanks for the symbols

 

[tiny-tim]

I was meant to say T = IA

Yeah, I thought so … but you don't need dA, then, do you?

(and anyway you can't have only one d … you can either have a d/d, or you can have a d on the LHS and another d on the RHS)

I was planing to integrate A to get the velocity

Yes, v = ∫ A dt.

(Remember, if you're integrating A, you don't put a d in front of it!)

 

[SpartanG345]

i understand the τ changes is angle and forms a sine wave with respect to θ

given that α = τ/I you could construct a graph of α vs θ

but i am not sure how to get α as a function of θ
do we have to start of with a dα

or

can we say α = qEdsin(θ)dθ/I
or can we say that α = qEdsin(θ)/I - is that correct do we even need a differential equation?

then i integrate α with respect to θ to get the angular velocity... not sure with this part, if you integrate α with respect to θ you will get the area under the αvθ graph

which represents the total acceleration...

is it possible to get the final angular velocity from a graph of α and θ?
as v = integral of α with respect to time?

thank you for you help by the way :)

 

[tiny-tim]

… do we even need a differential equation?

No, your torque equation already gives you α as a function of θ …

now you integrate to get ω.

(Hint: use the trick α = dω/dt = dω/dθ dθ/dt = ω dω/dθ )

 

[ehild]

What about to use conservation of energy? The potential energy of the dipole p in the electric field E is U=-p*E*cos(theta).

ehild