To calculate the pressure at the top and base of the cylinder, we first need to find the depth of the cylinder in the water.
Given:
Height of cylinder (h) = 0.30m
Area of cross-section (A) = 0.50m²
Density of water (ρ) = 1000 kg/m³
Acceleration due to gravity (g) = 9.81 m/s²
The volume of the cylinder can be calculated using the formula:
Volume = Area x Height
Volume = 0.50m² x 0.30m
Volume = 0.15m³
Since the mass of the cylinder is given as 100kg, we can calculate the density of the cylinder using the formula:
Density = Mass / Volume
Density = 100kg / 0.15m³
Density = 666.67 kg/m³
Since the density of the cylinder is less than the density of water, it will float at a height where the buoyant force equals the weight of the cylinder. Therefore, the volume of water displaced by the cylinder is equal to its volume.
Now, let h1 be the height of the cylinder submerged in water.
The weight of the cylinder can be calculated using the formula:
Weight = Mass x Acceleration due to gravity
Weight = 100kg x 9.81 m/s²
Weight = 981 N
The buoyant force acting on the cylinder is equal to the weight of the water displaced, which can be calculated using the formula:
Buoyant Force = Density of water x Volume of water displaced x Acceleration due to gravity
Buoyant Force = 1000 kg/m³ x Volume of water displaced x 9.81 m/s²
Since the volume of water displaced is equal to the volume of the cylinder, we have:
Buoyant Force = 1000 kg/m³ x 0.15m³ x 9.81 m/s²
Buoyant Force = 1471.5 N
At equilibrium, the weight of the cylinder is balanced by the buoyant force:
Weight = Buoyant Force
981 N = 1471.5 N
h1 = 0.20m
Therefore, the height of the cylinder submerged in water is 0.20m.
Now, we can calculate the pressure at the top and base of the cylinder.
Pressure at the top of the cylinder:
P_top = P_atm + ρgh_top
P_top = 1000 kg/m³ x 9.81 m/s² x 0.20m
P_top = 1962 Pa
Pressure at the base of the cylinder:
P_base = P_atm + ρgh_base
P_base = 1000 kg/m³ x 9.81 m/s² x 0.30m
P_base = 2943 Pa
Therefore, the pressure in excess of that due to the atmosphere at the top of the cylinder is 1962 Pa and at the base of the cylinder is 2943 Pa.
A solid cylinder,mass 100kg,is suspended in water between two tight cables so that the circular faces are horizontal and the upper face is 0.20m below the surface. The area of a circular cross-section of the cylinder is 0.50m² and it's height is 0.30m. The density of water is 1000kg/m³ .
1) Calculate the pressure in access of that due to the atmosphere at the top and at the base of the cylinder .
1 answer