Given that the tank is shaped like a right circular cylinder with a height of 30 m and with a base radius of 10m. The tank is attached to a steel cable of negligible mass and immersed in water. Calculate the tension (force) in the cable before and after it is immersed in water.
To calculate the tension in the cable before and after it is immersed in water, we need to consider the buoyant force acting on the tank.
Before immersion in water:
The tension in the cable before immersion can be calculated using the principle of equilibrium. The weight of the tank (force due to gravity acting on it) is balanced by the tension in the cable.
The weight of the tank is given by the formula:
Weight = mass * gravitational acceleration
The mass of the tank can be calculated using the formula:
Mass = density * volume
The density of steel is around 7850 kg/m^3, and the tank is in the shape of a right circular cylinder with a height of 30 m and a base radius of 10 m. So, the volume of the tank is given by the formula:
Volume = π * radius^2 * height
Now we can calculate the weight:
Weight = mass * gravitational acceleration
After immersion in water:
When the tank is immersed in water, it experiences a buoyant force due to the displacement of water. The buoyant force is equal to the weight of the water displaced by the tank.
The volume of water displaced by the tank is the same as its own volume. The volume of the tank is calculated as mentioned above.
The weight of the water can be calculated using the formula:
Weight = mass * gravitational acceleration
We need to substitute the mass of water with the density of water (around 1000 kg/m^3) and the volume of the tank.
Finally, the tension in the cable after immersion in water is equal to the difference between the weight of the tank and the buoyant force acting on it.