Translational and rotational kinetic energy-Mass Unknown

[Crusader711]

A hollow, thin-walled sphere (ICM = 2MR2/3) of mass 20 kg is completely filled with a liquid of unknown mass. The sphere is released at the top of a plane inclined at 30° to the horizontal, and it rolls 20 m to the bottom in 3.6 s. What is the mass of the liquid?



2.My approach is translational and rotational kinetic energy, first off. I know that for rolling spheres the v-cm is not dependent upon the mass nor radius of the objects. So I come up with a translational speed but I'm not certain where to go from there. But the problem wants the mass of the liquid. I have two different sphere's in theory, a solid and a thin-walled version.



3. Looking for a lead into the next step...

 

[tiny-tim]

Hi Crusader711!

I know that for rolling spheres the v-cm is not dependent upon the mass nor radius of the objects.

for a particular shape, yes

I have two different sphere's in theory, a solid and a thin-walled version.

But you're given the moment of inertia anyway.

Since we're not told the radius of the sphere, I think we're supposed to assume that the liquid does not rotate.

So find the acceleration, call the mass of the liquid "m", and carry on from there. ​

 

[Crusader711]

Rolling verses Frictionless

Would we treat the spheres differently?

thin-walled sphere rolling...

...then solid sphere with liquid, liquid sphere moving down incline (not rolling), but we have to account for the ICM of the thin-walled shell too?

Any thoughts?

 

[tiny-tim]

(just got up :zzz:)

i assume "ICM" means moment of inertia?

you are given the moment of inertia and the mass, why do you need to know anything else?