Finding Rotational Kinetic Energy of Sphere on Ramp

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Homework Help Overview

The problem involves calculating the total kinetic energy of a solid sphere rolling down a ramp. The sphere's mass and speed are provided, but there is uncertainty regarding the radius and its impact on the calculations.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between rotational and linear kinetic energy, questioning the necessity of the sphere's radius in the calculations. There are attempts to clarify the source of specific energy values and to verify calculations.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the calculations. Some guidance has been offered regarding the cancellation of the radius in the equations, but there is still confusion about specific energy values and their derivations.

Contextual Notes

There is a noted lack of clarity regarding the radius of the sphere, which is impacting the calculations. Participants are also reflecting on potential errors in their arithmetic or calculator usage.

joel amos
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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.
 
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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.
 
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
 
Where'd that 6.75 J come from?
 
izelkay said:
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
 
joel amos said:
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
 
haruspex said:
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.
 

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