Final answer:
The thrust at the bottom of the vessel is 18.6 N. The pressure at the bottom of the vessel is 310 Pa. The pressure at a depth of 5 cm from the free surface is 70 Pa. The net force experienced by the metal foil at a depth of 5 cm from the free surface is 1012550 N.
Step-by-step explanation:
To calculate the thrust at the bottom of the vessel, we need to find the weight of the liquid. The weight is equal to the density of the liquid multiplied by the volume of the liquid. Since the base area of the vessel is 100 cm x 60 cm and the height is 200 cm, the volume of the liquid will be 100 cm x 60 cm x 200 cm. To convert this volume to cubic meters, we divide by 100^3 to get 0.12 m x 0.06 m x 2 m = 0.14 m^3. Therefore, the weight of the liquid is (1.1 x 10^3 kg/m^3) * (0.14 m^3) * (9.8 N/kg) = 18.6 N. The thrust at the bottom of the vessel is equal to the weight of the liquid, which is 18.6 N.
To calculate the pressure at the bottom of the vessel, we divide the thrust by the base area of the vessel. The base area is 100 cm x 60 cm = 6000 cm^2. Multiplying by 1 m^2 / 10000 cm^2, we get 0.6 m x 0.1 m = 0.06 m^2. Therefore, the pressure at the bottom of the vessel is 18.6 N / 0.06 m^2 = 310 Pa. The pressure at the bottom of the vessel is 310 Pa.
To calculate the pressure at a depth of 5 cm from the free surface, we need to consider the weight of the liquid column above that depth. The weight is equal to the density of the liquid multiplied by the volume of the liquid column. Since the base area is the same, the volume of the liquid column is 100 cm x 60 cm x 5 cm. Converting this volume to cubic meters, we divide by 100^3 to get 0.12 m x 0.06 m x 0.05 m = 0.00036 m^3. Therefore, the weight of the liquid column is (1.1 x 10^3 kg/m^3) * (0.00036 m^3) * (9.8 N/kg) = 0.0042 N. The pressure at a depth of 5 cm from the free surface is equal to the weight of the liquid column divided by the base area of the vessel, which is 0.0042 N / 0.06 m^2 = 70 Pa.
To calculate the net force experienced by the metal foil at a depth of 5 cm from the free surface, we need to consider the pressure difference on both sides of the foil. The pressure at the top of the foil is atmospheric pressure, while the pressure at the bottom of the foil is the pressure at a depth of 5 cm from the free surface. The pressure at the top is 101325 Pa, and the pressure at the bottom is 70 Pa. Multiplying by the area of the foil, which is 10 cm^2, we get (101325 Pa - 70 Pa) * (10 cm^2) = 1012550 N. The net force experienced by the metal foil is 1012550 N.