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**1. Homework Statement**

the five objects of various masses, each denoted m, all have the same radius. They are all rolling at the same speed as they approach a curved incline.

Solid sphere - m = 1.0 kg

Hollow Sphere - m = 0.2 kg

Solid Cylinder - m = 0.2 kg

Solid Disk - m = 0.5 kg

Hoop - m = 0.2 kg

Rank the objects based on the maximum height they reach along the curved incline.

**2. Homework Equations**

Hoop - I=mr^2

Solid Disk and Cylinder - I=.5mr^2

Hollow Sphere - I=2/3mr^2

Solid Sphere - I=2/5mr^2

Where I is the moment of inertia, m is the mass, and r is the radius.

**3. The Attempt at a Solution**

I am unsure of where to go from here. I know the equations for inertia, but when I used the equation leaving out r^2 since they all have the same radius they were in the wrong order according to the website. What am I supposed to do?

I also know that the linear kinetic energy and the rotational kinetic energy are converted into gravitational potential energy. The equation I believe is 1/2mv^2 +1/2Iw^2 = mgh.

M is the mass, v is linear velocity, I is moment of inertia, w is angular velocity, g is gravity, and h is the height.

If I rearrange the equation to find height,

h=(1/2mv^2+1/2Iw^2)/mg

the masses cancel out leaving,

h=(1/2v^2 +1/2(r^2)(w^2))/ g

Am I on the right track? Am I forgetting something?

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