Calculate the % fan shaft is out of balance

[thewall]

Homework Statement

A fan loses an 11 gram piece 460mm from the shaft center. It rotates at 1000 RPM and cannot operate if the shaft is out of balance by more than 8%. Prove whether or not the fan can still operate.

Homework Equations

F_c = mwr²

The Attempt at a Solution

I have found the force added by the imbalance to be 55.5N but can't figure out how to relate this to a % of unbalance as I would need to know the mass of the whole fan blade assembly. I am thinking that 11 grams missing from a 1 kg fan blade would cause a higher percentage imbalance than it would in a 100 kg fan blade.

Could someone tell me if I am going about this problem the right way and if so how to do this, or do I need to take a different approach other than using centripetal forces.

Thanks for your time.

 

[LowlyPion]

Welcome to PF.

What does it mean to be 8% out of balance?

I take imbalance to mean in the dynamic sense that the axis of the moment of inertia (running through the center of gravity) is off set from the center of the fan shaft. But I am unfamiliar with the idea of what a % dynamic imbalance means.

As you note given a tremendously massive fan blade and a lightweight one this can mean very different things as regards the absolute displacement of the center of mass from the center of the shaft.

Hence fan blade length, mass distribution look to be additional facets of information required.

Is there any more information given with the problem?

 

[thewall]

There is no additional information supplied in the question.

I was unsure of what exactly what 8% out of balance meant as well. 8% of what? I was hoping someone could tell me.

If I work with forces or moments of inertia I still would need to somehow relate that to the original.