Percentage Uncertanty and youngs modulus

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To find the percentage uncertainty in d^3, the user has calculated the percentage uncertainty for the thickness of the strip as approximately 1.52%. They are unsure how to proceed with the uncertainties of the other measurements, specifically the mass and width. The user suggests that since the calculation involves d^3, the percentage uncertainty should be multiplied by three. The discussion highlights the importance of understanding propagation of uncertainty in calculations involving multiple variables. Clarification on how to combine the uncertainties for all measurements is needed to complete the solution.
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Homework Statement



hi there! I am new to this forum and was just wondering if anyone could help with this question on percentage uncertainty. I am supposed to find the percentage uncertainty in d^3

the info given is
mass attached to the end of a strip= 0.1 (+-0.001)kg
the width of the strip = 12.6 (+- 0.1)mm
the thickness of the strip= 0.66(+- 0.01)mm

Homework Equations


I am also given the equation for youngs modulus

E= 16pi^2 K^2 M/bd^3

The Attempt at a Solution



I worked out the percentage uncertainty of the thickness of the strip which was approx. 1.52% but am for completely lost:confused:

Thank You!
 
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so would i just simply multiply the percentage uncertainty by 3 as its d^3?
 
Sure, I'd buy that.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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