A problem about spherical pendulum that filled with water

[amirghaderi]

We have a hollow spherical pendulum that is filled with water. The sphere has a hole under it. If it starts to oscillate and at the beginning it was full of water, how it’s period would be by passing time and empting sphere?

 

[Hootenanny]

We have a hollow spherical pendulum that is filled with water. The sphere has a hole under it. If it starts to oscillate and at the beginning it was full of water, how it’s period would be by passing time and empting sphere?

Welcome to PF amirghaderi,

Well I suppose the first question to ask yourself is that what property changes as the water empties from the sphere?

 

[amirghaderi]

the mass and the inertia of the sphere changes

 

[Hootenanny]

the mass and the inertia of the sphere changes

Indeed it does. However, the problem is greatly simplified because usually a spherical pendulum is seen as a generalisation of a simple pendulum in three-space, which means that we can ignore the moment of inertia of the sphere and just consider the pendulum as a point mass suspended by a massless string.

EDIT: So, now you need to decide how the position of the centre of mass of the sphere varies with time.

 

[atavistic]

We only need to find the effective "l" for the pendulum which is the distance of the centre of mass from the point of attaching of the string.

 

[PhysicsDruid]

Hence... the problem. This sounds like some sort of twisted related rates problem. From the sort of question you posted, I imagine you know how to calculate your moments of inertia (and maybe are familiar with the tensor forms even)... sounds like you just need to express the rate of change of mass for the volume of water within the sphere. Neglecting the mass of the sphere itself, as Hottenanny already mentioned.

 

[amirghaderi]

i am graduated student in physics and i knonw how to calculate its moments of inertia but and how to simply ignore it as a point mass but i can't reach its answer that is first its period becomes large and then becomes smaler and without ignoreing the inertial momentom of the sphere solving becomes very complicated and did not look a meaning ful answer

 

[Hootenanny]

i am graduated student in physics and i knonw how to calculate its moments of inertia but and how to simply ignore it as a point mass but i can't reach its answer that is first its period becomes large and then becomes smaler and without ignoreing the inertial momentom of the sphere solving becomes very complicated and did not look a meaning ful answer

Consider where the centre of mass of the hollow sphere is located at the following points:

(a) When it is full of water
(b) When it is half full of water
(c) When it is empty

 

[amirghaderi]

thanx mr Hootenanny for your hint .
i solve it .
the period first increses and then retern to the orginal value

 

[Hootenanny]

thanx mr Hootenanny for your hint .
i solve it .
the period first increses and then retern to the orginal value

It's a pleasure