Respuesta :
Answer:
(a). The density of the wood is [tex]1479.48\times10^{2}\ Kg/m^3[/tex]
(b). The absolute pressure at the bottom of the tank is [tex]1.06200\times10^{5}\ Pa[/tex].
Explanation:
Given that,
Side of cube = 15.0 cm
Depth = 50 cm
Tension = 6.615 N
We need to calculate the volume of the wood
Using formula of volume
[tex]V = a^3[/tex]
[tex]V=(15.0\times10^{-2})^3[/tex]
[tex]V=0.003375\ m^3[/tex]
We need to calculate the density of the wood
Using buoyant force
[tex]\rho_{w}gh=mg+T[/tex]
[tex]\rho_{w}gh=\rho_{c}Vg+T[/tex]
Put the value into the formula
[tex]\rho_{c}=\dfrac{\rho_{w}gh-T}{Vg}[/tex]
Put the value into the formula
[tex]\rho_{c}=\dfrac{1000\times9.8\times50\times10^{-2}-6.615}{0.003375\times9.8}[/tex]
[tex]\rho_{c}=1479.48\times10^{2}\ Kg/m^3[/tex]
(b). We need to calculate the absolute pressure at the bottom of the tank
Using formula of absolute pressure
[tex]P=P_{atm}+\rho gh[/tex]
Put the value into the formula
[tex]P=1.013\times10^{5}+1000\times9.8\times0.5[/tex]
[tex]P=1.06200\times10^{5}\ Pa[/tex]
Hence, (a). The density of the wood is [tex]1479.48\times10^{2}\ Kg/m^3[/tex]
(b). The absolute pressure at the bottom of the tank is [tex]1.06200\times10^{5}\ Pa[/tex].
