Question

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 . Calculate the corresponding forces acting on each side of these faces and hence the net upward force due to the water pressure.

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, we need to calculate the volume of the cylinder:

Volume = Area of circular cross-section x height
Volume = 0.5m² x 0.3m
Volume = 0.15m³

Next, we calculate the weight of the cylinder:

Weight = mass x gravity
Weight = 100kg x 9.81 m/s²
Weight = 981N

Since the cylinder is in equilibrium, the net upward force due to water pressure must equal the weight of the cylinder. The net upward force is the difference between the forces acting on the top and bottom faces of the cylinder.

Let's first calculate the force acting on the top face of the cylinder:

Force top = Pressure x Area
Pressure = density x gravity x depth
Pressure = 1000kg/m³ x 9.81m/s² x 0.2m
Pressure = 1962N/m²

Force top = 1962N/m² x 0.5m²
Force top = 981N

Now, we calculate the force acting on the bottom face of the cylinder:

Force bottom = Pressure x Area
Pressure = density x gravity x depth
Pressure = 1000kg/m³ x 9.81m/s² x 0.5m
Pressure = 4905N/m²

Force bottom = 4905N/m² x 0.5m²
Force bottom = 2452.5N

Net upward force = Force top - Force bottom
Net upward force = 981N - 2452.5N
Net upward force = -1471.5N

The negative sign indicates that the net upward force is acting downward. This means that the weight of the cylinder is greater than the net upward force due to the water pressure, which is why it is not floating.