Calculating Angular Acceleration of Hollow Sphere with Pressure Difference

[WhoThat3]

Homework Statement

Info on object:
Mass = 10kg
Radius = 0.20m
Lenght of spouts = 0.10m above surface of sphere. (The two spouts can be considered massless.)

The sphere is hollow and looks like this. The pressure inside is 1.5 atm and the pressure outside is 1.0atm.
http://upload.wikimedia.org/wikipedia/commons/3/3e/Aeolipile_illustration.JPG

a) Find moment of inertia (found)

b) What is the angular acceleration of the container? Take the area of the spouts to be circles of radius 0.010m.

Homework Equations

Not sure, but I used Pascals principle.
Bernoullis came to mind, but I doubt it.

The Attempt at a Solution

a) I = 2/3*MR^2 = 0.26...
I = 0.27

b) Pout = Pin(not sure since this is not true since pressure inside is 1.5atm pressure outside is 1.0atm)

Fout/Aout = Fin/Ain
Fout/(pi*r^2) = 1.5atm/(pi*r^2)
Fout=1.5atm

1.5atm = 151950 N/m^s
This is a tangental force...

F=mra (a is alpha, angular acceleration; r+lenght of spouts)

a=F/(mr)
a=50650?

Does not look right

I am a bit confused on what to use for part b of this question. I do not think that my result is accurate. Any advice would be appreciated or any pointers.
Thanks

edit: Also anyone know how to find the energy stored by the steam inside the container??

 

[Doc Al]

Since the inside pressure is greater than the outside pressure, there's a net outward force. Find that force and the resulting torque on the sphere.

 

[WhoThat3]

Hmm, ok I will try to find it, so I guess what I did was wrong then. Well cool, I'll post if I come across any other problems.

 

[WhoThat3]

Sorry for bringing this up again, but I can't find the force due to the pressures. Can someone tell me how to find it please, no need for a blunt answer, but a formula to use would do just as well? After this I am pretty sure I can finish the problem on my own.

 

[Doc Al]

What's the definition of pressure?

 

[WhoThat3]

pressure: Force/Area

 

[Doc Al]

Exactly. Note that they give you the area of the spouts. You have the net pressure and the area, so find the force exerted at each spout by the escaping steam.

 

[WhoThat3]

Ohh, ok so the force would be,

F = P*A
F = 1.5*(pi*r^2)
F = 0.00471

So now for torque:

t = r * F
t = (0.2m+0.1m) * 0.00471
t = 0.200047

Lastly
sigma t = I*a
a = sigma t/I

a = 0.108025

OK this sounds like a more reasonable answer thanks for the help. Now I only need to find the energy inside the container...sigh =)

 

[Doc Al]

Ohh, ok so the force would be,

F = P*A
F = 1.5*(pi*r^2)
F = 0.00471

The net pressure is not 1.5 atm--use the difference in pressure between inside and outside. But convert to standard units in order to find the force.

Would I need to double this since it does occur in two place but pushes in the same direction?

Both spouts are identical and exert the same torque. So figure it out for one and then double it.

 

[WhoThat3]

Ohh ok thanks, I fixed it, now to find the energy by the steam...would you help me with that as well?

 

[WhoThat3]

I guess no one knows this, well thanks for the help on the other parts guys =)