Question

A horizontal metal plate of area 0.50 m² lies at the bottom of a lake at a depth of the density of water is 1000 kg/m³ and the gravitational field strength g is 10 N. What is the downward force acting on the plate due to the water?

Answer 1

The downward force on the metal plate at the bottom of the lake can be calculated using the formula for hydrostatic pressure, resulting in a force of 200,000 N.

Step-by-step explanation:

The student is asking about the force exerted on a metal plate at the bottom of a lake. To calculate the downward force (hydrostatic pressure) acting on the plate due to the water above, we can use the formula Pressure (P) = Density (ρ) × Gravitational field strength (g) × Depth (h). The resultant force is then found by multiplying the pressure by the area of the object (Force (F) = P × Area (A)). Given that the density of water is 1000 kg/m³ and the gravitational field strength is 10 N/kg, and assuming the depth of the lake above the plate is 40.0 m, we can calculate the force:

F = ρghA = (1000 kg/m³)(10 N/kg)(40.0 m)(0.50 m²) = 200,000 N.

Thus, the downward force on the plate is 200,000 N.