Maximizing Vertical Height in Frictionless Rolling Motion on an Incline

[John Kolby]

Homework Statement

A hollow sphere of mass M and radius R (I = 2MR2 /3) is released from rest at height h and rolls down a curved surface without slipping until it reaches the lowest point, O..

The curve to the right of O is frictionless. If the sphere continues past point O, what vertical height will it reach?
(In the diagram, the curve looks like a semi circle)

Homework Equations

KE_r = 1/2 M W²
KE_l = 1/2MV²

The Attempt at a Solution

According to my knowledge, if its frictionless and energy is conserved it should reach the same high.

mgh = 1/2 M W² + 1/2MV²
**If I did something wrong I apologize, first time on this forum

 

[SammyS]

Homework Statement

A hollow sphere of mass M and radius R (I = 2MR2 /3) is released from rest at height h and rolls down a curved surface without slipping until it reaches the lowest point, O..

The curve to the right of O is frictionless. If the sphere continues past point O, what vertical height will it reach?
(In the diagram, the curve looks like a semi circle)

Homework Equations

KE_r = 1/2 M W²
KE_l = 1/2MV²

The Attempt at a Solution

According to my knowledge, if its frictionless and energy is conserved it should reach the same high.

mgh = 1/2 M W² + 1/2MV²

**If I did something wrong I apologize, first time on this forum

Hello John Kolby. Welcome to PF !

Does the rotation of the sphere change once it gets to the frictionless part of the curve?

Does its rotation correspond to some amount of kinetic energy?

 

[John Kolby]

Does the rotation of the sphere change once it gets to the frictionless part of the curve?

Does its rotation correspond to some amount of kinetic energy?

I don't think the rotation changes. The rotation accounts to K_r which I account for with 1/2MW²

 

[John Kolby]

Solved it thank you!