How to solve rotational work and energy problem?

[Ailiniel]

Homework Statement

Starting from rest, a basketball rolls from the top of a hill to the bottom, reaching a translational speed of 6.12 m/s. Ignore frictional losses.

Homework Equations

(a) What is the height of the hill?

(b) Released from rest at the same height, a can of frozen juice rolls to the bottom of the same hill. What is the translational speed of the frozen juice can when it reaches the bottom?

The Attempt at a Solution

Initial Total mechanical energy = Final Total mechanical energy
1/2mv^2 + 1/2IW^2 + mgh = 1/2mv^2 + 1/2IW^2 + mgh
Initial KE = 0 and final PE = 0
mgh = 1/2mv^2 + 1/2IW^2
gh = 1/2v^2 + 1/2IW^2

I am stuck with 2 unknown variables W and h.

 

[Doc Al]

Hint: Assuming each object rolls without slipping, what's the relationship between v and W?

Also: What's the rotational inertia of each object?

 

[Ailiniel]

mgh = 1/2mv^2 + 1/2IW^2
Tangent Velocity = rW
W=Tangent V / r

Substitute W and solve for h.
h = (1/2V^2 + 1/3(Tangent V)^2) / g

Tangent V = translational V

h=3.18

I got it now, Thanks!

 

[Doc Al]

Is Tangent velocity the same as translational velocity?

Yes, because it rolls without slipping.

 

[Doc Al]

I got it now, Thanks!

Good!