An evacuated spherical diving bell containing a camera is in the ocean at a depth of 107 m. It has a flat, transparent, circular port with a diameter of 10.5 cm. Find the magnitude of the total force on the port. For the density of seawater use 1025 kg/m3.

find the pressure at 107 meters, consider it constant over the port.

Pressure = one atmosphere + rho g h

= 10^5 pascals + 1025 * 9.8 * 107

= 10^5 + 10.75*10^5 = 11.75*10^5 Pascals or N/m^2

Force = 11.75 * 10^5 * area
= 11.75 (pi * .0525^2)*10^5
=.0996 *10^5
= 9960 N

To find the magnitude of the total force on the port of the diving bell, we can use the concept of pressure and apply it to the surface area of the port.

1. Calculate the pressure at the depth of the diving bell:
The pressure at a certain depth in a fluid can be calculated using the formula:
pressure = density × gravity × depth

Given:
Density of seawater (ρ) = 1025 kg/m³
Depth (h) = 107 m
Acceleration due to gravity (g) = 9.8 m/s²

Let's substitute the values and calculate the pressure at the depth:
pressure = 1025 kg/m³ × 9.8 m/s² × 107 m

2. Determine the force on the port:
The force on a surface can be calculated by multiplying the pressure by the surface area.

Given:
Diameter of the port (d) = 10.5 cm = 0.105 m
Radius of the port (r) = d/2 = 0.105 m / 2 = 0.0525 m

The surface area of the port (A) can be calculated using the formula for the area of a circle:
A = π × r²

Let's calculate the surface area of the port:
A = π × (0.0525 m)²

Finally, we can find the magnitude of the total force on the port by multiplying the pressure by the surface area:
Total Force = pressure × A

Substitute the values and calculate the magnitude of the total force on the port.

To find the magnitude of the total force on the port of the diving bell, we can use the formula for the hydrostatic pressure.

The hydrostatic pressure is given by the formula:

P = ρ * g * h

Where:
P is the pressure,
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the depth.

In this case, the fluid is seawater, so the density ρ = 1025 kg/m³. The depth h = 107 m, and the acceleration due to gravity, g, is approximately 9.8 m/s².

Let's calculate the pressure acting on the circular port:

P = ρ * g * h
= 1025 kg/m³ * 9.8 m/s² * 107 m
≈ 1,127,999 N/m²

The magnitude of the total force on the port is equal to the pressure multiplied by the area of the port.

To find the area of the port, we can use the formula for the area of a circle:

A = π * r²

Where:
A is the area of the port, and
r is the radius of the port, given by half the diameter.

The diameter of the port is 10.5 cm, so the radius r = 10.5 cm / 2 = 5.25 cm = 0.0525 m.

Now we can calculate the area of the port:

A = π * r²
= π * (0.0525 m)²
≈ 0.0086 m²

Finally, we can calculate the magnitude of the total force on the port:

Force = Pressure * Area
= 1,127,999 N/m² * 0.0086 m²
≈ 9,715.4 N

Therefore, the magnitude of the total force on the port is approximately 9,715.4 Newtons.