a solid sphere a hollow sphere and disk of same mass m and radius r are placed on top of incline and released from rest. the friction co-efficients are same but not sufficient enough to allow pure rolling. least time will be taken to reach the bottom by ?

Question

vincent-lyon.fr · Answer

Have you already worked out the accelerations of the three bodies?

vincent-lyon.fr · Answer

Have you already done the same problem when the 3 bodies have a pure rolling motion?

anonymous · Answer

yes in that case the solid sphere took the least time followed by the hollow one and the disk

vincent-lyon.fr · Answer

Correct!

Now write N's 2nd law in this new case and you will immediately see which arrives first.

anonymous · Answer

ok so the force due to gravity causes same acceleration in case of all the bodies and frictional force is also kinetic in here ..so they should all take the same time? (the angular acceleration doesn't matter in this case i guess ! )

anonymous · Answer

i mean frictional force is also same..so acceleration of centre of mass same?

vincent-lyon.fr · Answer

Correct, because, as they have the same weight, normal force will be the same and friction will be the same too.

So they will have the same acceleration, hence the same velocity and motion.

Can you find what the difference will be then?

anonymous · Answer

the kinetic energy would vary i guess at the bottom of the incline as also the angular velocity?

vincent-lyon.fr · Answer

Exactly, they will not rotate at the same rate. They will not have the same KE, but the energy lost by friction is not so easy to work out.

anonymous · Answer

ok but can an idea be made about which one will have the least kinetic energy?

ksaimouli · Answer

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ksaimouli · Answer

use newton mechanics or energy's

ksaimouli · Answer

$$u=\frac{ 1 }{ 2 }mv^2+\frac{ 1 }{ 2 }I \omega^2$$

ksaimouli · Answer

I is movement of inertia use those to calculate the velocities at the bottom

vincent-lyon.fr · Answer

I think the one with the greatest moment of inertia (the disk) will tend to rotate slowest. For the disk, the slipping velocity will be greatest and so will the power lost to friction.
So the disk will have the smallest KE when it reaches the bottom of the inclined plane.

anonymous · Answer

for pure rolling motion kinetic energy was found to be the translational kinetic energy+rotational kinetic energy ..does this thing apply in here too?

vincent-lyon.fr · Answer

Yes, it does.

anonymous · Answer

ok got it perfectly..thanx!

anonymous · Answer

and can you help me with this one i asked earlier? http://openstudy.com/study#/updates/50e75bb7e4b06af148a03c9c