Submerged 81714

A concrete column with a density of 3500 kg/m³, a height of 6 m, and a square base of a=25 cm lies at the bottom of the dam at a depth of 10 m. At the upper end, it is lifted by a rope by a crane. 1) with how much force does the pole stretch the rope if the entire pole is submerged in water? 2) how much force does the pole exert on the rope if it is entirely in the air?

Correct answer:

F₁ =  9196.875 N
F₂ =  12875.625 N

Step-by-step explanation:

$$\begin{gathered} \rho =3500{\text{kg/m}}^3 \\ {\rho }_2=1000{\text{kg/m}}^3 \\ h=6\text{m} \\ a=25\text{cm}\to \text{m}=25:100\text{m}=0.25\text{m} \\ {h}_2=10\text{m} \\ g=9.81{\text{m/s}}^2 \\ {S}_1=a^2=0.25^2=\frac{1}{16}=0.0625{\text{m}}^2 \\ V=S_1\cdot h=0.0625\cdot 6=\frac{3}{8}=0.375{\text{m}}^3 \\ m=\rho \cdot V=3500\cdot 0.375=\frac{2625}{2}=1312.5\text{kg} \\ {m}_2={\rho }_2\cdot V=1000\cdot 0.375=375\text{kg} \\ {F}_2=m\cdot g=1312.5\cdot 9.81=\frac{103005}{8}=12875.625\text{N} \\ {F}_3=m_2\cdot g=375\cdot 9.81=\frac{14715}{4}=3678.75\text{N} \\ {F}_1=F_2-F_3=12875.625-3678.75=9196.875\text{N} \end{gathered}$$

$F_2=12875.625=12875.625\text{N}$

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