Final answer:
The hydrostatic force on the submerged car door can be determined using the product of hydrostatic pressure and the area of the door. The pressure center is found by calculating the centroid of the pressure distribution on the door, which is generally below the geometric center due to increasing pressure with depth.
Step-by-step explanation:
The hydrostatic force on the door of a submerged car can be calculated using the formula for the hydrostatic pressure, P = ρgh, where ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the fluid. The force, F, exerted on the door is then F = P x A, where A is the area of the door. The location of the pressure center is where the total moment due to the hydrostatic pressure is equivalent to the moment produced by the total force acting at the pressure center. It is generally located below the centroid of the submerged surface due to the increase of pressure with depth.
To solve the problem, since the question states that the upper edge of the door is 8 m underwater, we can take the average depth to be h = 8.55 m (since the door is 1.1 m high, the mid-point will be half of this height, which is 0.55 m). Using 1000 kg/m³ for the density of water and 9.81 m/s² for g, you would multiply the average P by the area of the door (1.1 m x 1.3 m) to find F. To find the location of the pressure center, you need to set up an integral as the pressure varies with depth and solve for the centroid of the pressure distribution.