Rotational Motion-Up an Incline

1. The problem statement, all variables and given/known data

A solid sphere (S), a thin hoop (H), and a solid disk (D),
all with the same radius, are allowed to roll down an
inclined plane without slipping. At the bottom, they run into another inclined plane and begin rolling upwards. Which will travel the furthest up the inclined plane, neglecting all frictional forces?

Thin Hoop KE=1/2mv^2 + 1/2(MR^2)w^2

Solid Sphere KE=1/2mv^2 + 1/2(2/5MR^2)w^2

Solid Disk KE=1/2mv^2 + 1/2(1/2MR^2)w^2

2. Relevant equations

1/2mv^2 + 1/2Iw^2 = mgh


3. The attempt at a solution

A previous question had asked which reaches the bottom first and I had found that to be the sphere, followed by the disk, and finally the thin hoop. I suspect that the sphere would travel the furthest up the incline because it has the greatest KE at the bottom of the first incline, but I am unsure if this assumption is correct.

Thank you for the help!
 

tiny-tim

Science Advisor
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Welcome to PF!

Hi abspeers! Welcome to PF! :smile:
… I suspect that the sphere would travel the furthest up the incline because it has the greatest KE at the bottom of the first incline, but I am unsure if this assumption is correct.
You're right, it's not correct …

never mind the KE at the bottom, its the KE and PE at the start that matters, isn't it? :wink:
 

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