Finding Rotational Kinetic Energy of Sphere on Ramp

[joel amos]

Homework Statement

If Inga, the Laboratory Assistant, rolls a spare head down a 4 m ramp because it was spherical and solid and too heavy at 4.5 kg at a speed of 4.5 m/s, what was its total kinetic energy?

Homework Equations

KE = (1/2) I ω^2
I = (2/5) MR^2

The Attempt at a Solution

Basically, I'm not sure how to solve this without the sphere's radius. Any help, solutions, or hints would be highly appreciated.

 

[haruspex]

Just go ahead with the algebra and you should find the radius cancels out. The rotational KE of a sphere is in fixed ratio to its linear KE, regardless of radius.

 

[joel amos]

So does this look correct:

KE = (1/2)(4.5 kg)(4.5m/s)^2 + (1/2)(2/5)(4.5)r^2[(4.5m/s)/r]^2
KE = 6.75 J + 18.225 J
KE = 24.98 J

 

[izelkay]

Where'd that 6.75 J come from?

 

[joel amos]

Where'd that 6.75 J come from?

Hmm..I too am now wondering the same.

Is this better:

KE = 45.453 J + 18.225 J
KE = 63.69 J

 

[haruspex]

Hmm..I too am now wondering the same.

Is this better:

KE = 45.453 J + 18.225 J
KE = 63.69 J

Still a bit low. I get 45.56+18.23=63.79

 

[izelkay]

Still a bit low. I get 45.56+18.23=63.79

That's also what I'm getting. Joel, I think you're not plugging into your calculator correctly.