Analysis for Water

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As with water (the process is exactly the same), the only equation that is truly needed to solve this problem is

 

F_B=\rho_fgAH 

 

Once we know the slope, (which in this case is \frac{F_b}{H}), we can set the slope equal to \rho_fg\pi r^2

However, in this case it is convenient to multiply the slope by 100 to change it to N/M. This, coupled with changing the measured radius to meters, will give a final result in KG/M

 

m= 2.914 N/cm

r=.0095 M

Therefore, 

 

m=\rho_fg\pi r^2

 

\frac{m}{g\pi r^2}=\rho_f

 

with units:

\frac{2.914\left(\frac{N}{m}\right)}{9.8\left(\frac{N}{Kg}\right)\cdot\pi\cdot\left(.0095\left(m\right)\right)^2}=\rho_f

 

\rho_f=\frac{1048.74\:Kg}{m^3}

 

From this, our percent error is shown by:

 

 \frac{\mid 1000-1048.74\mid }{1000}\cdot100=4.87\%\:error

 

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