Conservation of energy in rotational motion

[mit_hacker]

Homework Statement

(Q) A uniform marble rolls down a symmetric bowl, starting from rest at the top of the left side. The top of each side is a distance h above the bottom of the bowl. The left half of the bowl is rough enough to cause the marble to roll without slipping but the right half is frictionless.

(a) How far up the smooth side will the marble go, measured vertically from the bottom?

(b) How high up would the marble go if both sides were as rough as the left hand side?

(c) How do you account for the fact that the marble goes higher up with friction on the right side than without friction?

Homework Equations

KE = (1/2)MV^2 + (1/2)IcmW^2.
PE = mgh

The Attempt at a Solution

I am completely blank.
How do I account for the friction on just the right hand side?
Since the bowl is symmetrical, can I take its radius to be h?
Is it ok to say that the angular displacement of the marble is pi/2 from top to bottom?

Pleeeaseeeee help!

 

[learningphysics]

initial energy = mgh

bottom of the bowl, energy is (1/2)MV^2 + (1/2)IcmW^2.

relate W to V...

what do you get for V?

when it goes up the frictionless side what happens to the translational energy? what happens to the rotational energy?

 

[mit_hacker]

Friction?

What about friction? Don't we deduct that from the expression

(1/2)MV^2 + (1/2)IcmW^2 to get (1/2)MV^2 + (1/2)IcmW^2 -fD where f is force of friction?

Why don't we take that into account?

 

[learningphysics]

What about friction? Don't we deduct that from the expression

(1/2)MV^2 + (1/2)IcmW^2 to get (1/2)MV^2 + (1/2)IcmW^2 -fD where f is force of friction?

Why don't we take that into account?

friction only does work when the surfaces slide against each other... in this case it is rolling without any sliding... no energy is lost.

work by friction = frictional force*distance (this is the distance the point of application moves... but in this case there is no slipping, the point of application doesn't move at all... distance = 0).

 

[mit_hacker]

Thanks!

Hey, thanks a ton for that! I never knew that in rolling, friction does not do any work. Again, thanks a ton!

 

[learningphysics]

Hey, thanks a ton for that! I never knew that in rolling, friction does not do any work. Again, thanks a ton!

no prob. :)