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?

 

[Nickie]

I would approach this problem by using the principles of kinetic energy to determine the mass of the liquid. First, I would calculate the translational kinetic energy (KE) of the sphere using the formula KE = 1/2 * m * v^2, where m is the mass of the sphere and v is the translational speed.

Next, I would calculate the rotational kinetic energy (KE) of the sphere using the formula KE = 1/2 * I * ω^2, where I is the moment of inertia of the sphere and ω is the angular velocity.

Since the sphere is rolling without slipping, the total kinetic energy of the system is the sum of the translational and rotational kinetic energies. Therefore, I can equate the two equations and solve for the unknown mass of the liquid.

However, in order to do this, I need to know the moment of inertia of the sphere. The given information tells us that the sphere is a hollow, thin-walled sphere with a moment of inertia of ICM = 2MR^2/3. Using this information, I can calculate the moment of inertia and substitute it into the equation to solve for the unknown mass of the liquid.

Once I have the mass of the liquid, I can then use this information to determine other properties of the system, such as the density of the liquid or the total kinetic energy of the system. This approach allows me to use the principles of translational and rotational kinetic energy to solve for the unknown mass in a systematic and scientific way.