Odpowiedź:
Zad. 1
[tex]V_{z} =\frac{7}{8} V\\\rho_w=1000\frac{kg}{m^3}\\\\\rho =\frac{m}{V} \Rightarrow m= \rho_{c} \cdot V\\F_{g} = m \cdot g =\rho_{c} \cdot V\cdot g\\F_{w}= \rho_{w}\cdot V_{z}\cdot g\\F_{g}=F_{w}\\\rho_{c} \cdot V\cdot g=\rho_{w}\cdot V_{z}\cdot g\\\rho_{c} \cdot V\cdot g=1000 } \cdot \frac{7}{8} V\cdot g ~~/:g\\\rho_c \cdot V= 875V~~ /:V\\\rho_c=875\frac{kg}{m^3}[/tex]
Zad. 2
[tex]\rho_c=300\frac{kg}{m^3}\\\rho_w=1000\frac{kg}{m^3}\\\\\rho =\frac{m}{V} \Rightarrow m= \rho_{c} \cdot V\\F_{g} = m \cdot g =\rho_{c} \cdot V\cdot g\\F_{w}= \rho_{w}\cdot V_{z}\cdot g\\F_{g}=F_{w}\\\rho_{c} \cdot V\cdot g=\rho_{w}\cdot V_{z}\cdot g\\300V\cdot g=1000V_z\cdot g ~~ /:g \\300V=1000V_z ~~/:1000\\V_z=\frac{300}{1000}V\\V_z=0,3V[/tex]
Zad. 3
[tex]h_1=20cm\\h_2=47cm\\\rho_1=1000\frac{g}{cm^3}\\\\p_1=p_2\\\rho_1\cdot g\cdot h_1=\rho_2\cdot g\cdot h_2\\1000\cdot g\cdot 20 = \rho_2\cdot g\cdot 47~~/:g\\20~000=47\rho_2~~/:47\\\rho_2\approx 425,53\frac{g}{cm^3}[/tex]
Zad. 4
[tex]\rho_1 = 920\frac{kg}{m^3}\\\rho_2=1500\frac{kg}{m^3}\\\\p_1=p_2\\\rho_1\cdot g \cdot h_1=\rho_2\cdot g \cdot h_2~~/:g\\\rho_1\cdot h_1=\rho_2\cdot h_2\\\frac{h_1}{h_2}=\frac{\rho_2}{\rho_1}\\\frac{h_1}{h_2}=\frac{1500}{920}\\\frac{h_1}{h_2}=\frac{75}{46}=1\frac{29}{46}\approx 1,63[/tex]
