Question

In 1708, Galeon San Jose, a Spanish ship laden with treasure, sank to the bottom of the sea, 1000 m below the surface. Find the force on one side of a 6 m square plate at the depth of the ship if the plate is:

A. Lying horizontally: F= ___ N.

Answer 1

The force on one side of a square plate at the depth of the ship is 3.528 x 10^8 N.

Step-by-step explanation:

To find the force on one side of a square plate at the depth of the ship, we can use the concept of pressure. The force on one side of the plate is equal to the pressure exerted by the water multiplied by the area of the plate. Pressure is calculated using the formula P = ρgh, 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 depth is 1000 m below the surface, so h = 1000 m. The density of water is approximately 1000 kg/m³. The acceleration due to gravity is 9.8 m/s². The area of the plate is 6 m x 6 m = 36 m².

Plugging in the values, we get P = (1000 kg/m³)(9.8 m/s²)(1000 m) = 9.8 x 10^6 Pa. To find the force, we multiply the pressure by the area of the plate: F = (9.8 x 10^6 Pa)(36 m²) = 3.528 x 10^8 N.

Answer 2

To find the force on one side of a 6 m square plate lying horizontally 1000 m below the sea surface, calculate the pressure at that depth and multiply it by the area of the plate, resulting in a force of 3.60×10⁸ N.

Step-by-step explanation:

The question involves finding the force on one side of a 6 m square plate lying horizontally at the depth of 1000 m below the sea surface. To calculate this force, we need to use the formula for pressure exerted by a fluid at a certain depth, which is P = ρgh, where ρ is the density of seawater (approximately 1025 kg/m³), g is the acceleration due to gravity (9.81 m/s²), and h is the depth below the surface. After calculating the pressure, we multiply it by the area of the plate to find the force.

The pressure exerted by the seawater at a depth of 1000 m is P = (1025 kg/m³)(9.81 m/s²)(1000 m) = 1.00×10⁷ Pa (pascals). The area of the 6 m square plate is A = 6 m × 6 m = 36 m². The force on the plate is then F = PA = (1.00×10⁷ Pa)(36 m²) = 3.60×10⁸ N (Newtons).