Find average velocity of a sphere which expands and moves

[haruspex]

Ok yeah yeah you are right.Is that all thing somy equatipn is true If I change r to v ?

There are some more errors. The m at the front should be $\rho r^2$, where $\rho$ is the density. There should be a factor $\sin(\theta)$ inside the integral (or maybe it's $\sin(\theta)$, whichever goes from 0 to $\pi$). This comes from the polar expression for an area element.

 

[Quarlep]

ρr²((v')2+v^2+2π^2)+ integral sinθ from 0 to π

 

[haruspex]

ρr²((v')2+v^2+2π^2)+ integral sinθ from 0 to π

Better, but that 2π^2 term shouldn't be there. Previously, every term had a factor of either v or v', so that should remain true. Instead, I would expect to see a factor π throughout. Please post all your steps.

 

[Quarlep]

Are you there my friend

 

[haruspex]

Are you there my friend

We're in different timezones, I'm sure. But I did reply to your post #72. Can you not see my reply?

 

[Quarlep]

There are some more errors. The m at the front should be $rho r^2$, where $rho$ is the density. There should be a factor $\sin(\theta)$ inside the integral (or maybe it's $\sin(\theta)$, whichever goes from 0 to $\pi$). This comes from the polar expression for an area element.

Hi I see your post but I couldn't answer cause I am in holiday now and here time is 07:20 am. In this post you said $\sin(\theta)$ will be inside the integral but theta goes 0 to pi so here I am confused and I ll going to write pr^2 instead of m ?

 

[haruspex]

Hi I see your post but I couldn't answer cause I am in holiday now and here time is 07:20 am. In this post you said $\sin(\theta)$ will be inside the integral but theta goes 0 to pi so here I am confused and I ll going to write pr^2 instead of m ?

In your integrand you have trig functions of phi and theta. But you must have put the area element as $m d\theta d\phi$. The area element should have been $\rho r^2 \sin(\theta)d\theta\phi$. After simplifying the rest of the integrand, you still have one term left that has trig functions in it. You must multiply the sin from the element with this before integrating it.
This will be a lot easier to explain if you post all your steps as typed equations. Please stop posting images of working, they're too hard to read and too hard to make comments about.

 

[Quarlep]

http://www.HostMath.com/Show.aspx?I...hi)^2+\int_{0}^{\pi}pr^2\sin\thetad\theta\phi look

 

[Quarlep]

I made a mistake in there.Can you write the correct one and send me like this url then I can work on it

 

[haruspex]

http://www.HostMath.com/Show.aspx?IsAsc=True&Code=\int_{0}^{\pi}\int_{0}^{2\pi}(v\cos\theta\sin\phi+v')^2+(v\sin\theta\sin\phi)^2+(v\cos\phi)^2+\int_{0}^{\pi}pr^2\sin\thetad\theta\phi look
$\int_{0}^{\pi}\int_{0}^{2\pi}(v\cos\theta\sin\phi+v')^2+(v\sin\theta\sin\phi)^2+(v\cos\phi)^2+\int_{0}^{\pi}pr^2\sin\theta d\theta\phi$

That equation makes no sense syntactically. It should read
$\int_{\theta=0}^{\pi}\int_{\phi=0}^{2\pi}((v\cos\theta\sin\phi+v')^2+(v\sin\theta\sin\phi)^2+(v\cos\phi)^2)\rho r^2\sin\theta d\theta d\phi$

 

[Quarlep]

Yeah I noticed that pr^2 must be inside the integral I noticed it after I wrote the equation

 

[Quarlep]

Can you check the integral again I think there's a wrong something

 

[haruspex]

Can you check the integral again I think there's a wrong something

Wrong in my version? I don't see anything - please be more specific.

 

[Quarlep]

Theres two integral first one belongs theta second phi but then end you wrote d theta phi

 

[Quarlep]

I find 2pr²((v')²)+2πv²)

 

[haruspex]

Theres two integral first one belongs theta second phi but then end you wrote d theta phi

It's a double integral. Have you not dealt with double integrals before?

 

[Quarlep]

No

 

[Quarlep]

Did you see my answer ?.Or its wrong

 

[haruspex]

Did you see my answer ?.Or its wrong

It's wrong. Please post all your steps.

 

[Quarlep]

Can dtheta and dphi change sides

 

[haruspex]

Can dtheta and dphi change sides

Do you mean, can they be in either order? Yes. It's the order of the integral signs that defines the order of integration (inside first).

 

[Quarlep]

I am in holiday I am not working in computer so I can't write all steps to you right now.We will do first integral (the one which is inside) that's phi but there wrote dtheta so I asked you this

 

[Quarlep]

Can you tell me what was that please the only thing I ll do is put it on program

 

[haruspex]

Can you tell me what was that please the only thing I ll do is put it on program

Sorry, I don't understand what you are asking.

 

[Quarlep]

The answer :):)

 

[haruspex]

The answer :):)

Do you simply want the answer to the original question, by whatever means, or do you specifically want to see how to do it through an elaborate double integral?

 

[Quarlep]

I want to see answer to the original question

 

[Quarlep]

I am working on symbolab but I found nothing

 

[haruspex]

I want to see answer to the original question

Then use my symmetry method. It gets rid of the trig terms and makes the integral trivial.

 

[Quarlep]

I was banned so I couldn't answer over a 10 days I found 4p(pi)r^2((v'^2)+v^2)

 

[haruspex]

I was banned so I couldn't answer over a 10 days I found 4p(pi)r^2((v'^2)+v^2)

I think it should be exactly half that.
Note that the factor outside the parentheses is just the mass.

 

[Quarlep]

Thank you so much. Problem is solved now.