A problem about angular momentum

[VictoriaWoo]

Homework Statement

A marble of mass M and radius R is rolled up a plane of angular θ. If the initial velocity of the marble is v, what is the distance l it travels up the plane before it begins to roll back down?

Homework Equations

The Attempt at a Solution

I would like to know the details of the motion. The answer is l≈1.3m. But I try the equation -mglsinθ=0-(1/2m^v+1/2I^ω), the result is about 1.5m. I know it is not the correct way, but I am just confused about the critical condition and how the friction is canceled out.

 

[tiny-tim]

energy?

 

[VictoriaWoo]

There is no information about energy in the question offered in An Introduction To Mechanis by Kleppner.

 

[tiny-tim]

yes there is …

you know m and v and I and ω, so you know the kinetic energy ! ​