Question

A cube with 30-cm-long sides is sitting on the bottom of an aquarium in which the water is one meter deep. (Round your answers to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.) (a) Estimate the hydrostatic force on the top of the cube. N (b) Estimate the hydrostatic force on one of the sides of the cube. N

Answer 1

The hydrostatic force on the top of the cube is approximately 882 N, and the hydrostatic force on one of the sides is also approximately 882 N.

Step-by-step explanation:

When an object is submerged in a fluid, it experiences a hydrostatic force due to the pressure exerted by the fluid.

For the top of the cube, the hydrostatic force can be calculated by multiplying the pressure at that depth with the area of the top surface. The pressure at a depth of 1 meter is given by the formula P = ρgh, where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid. Using the given values, we have:

P = (1000 kg/m³)(9.8 m/s²)(1 m) ≈ 9800 N/m².

The area of the top surface of the cube is (30 cm)² = 900 cm². Converting to square meters, we get 0.09 m². Multiplying the pressure by the area gives us the hydrostatic force on the top of the cube:

Hydrostatic force = (9800 N/m²)(0.09 m²) ≈ 882 N.

For one of the sides of the cube, the hydrostatic force can be calculated in the same way. The area of one side is also 900 cm² or 0.09 m². Therefore, the hydrostatic force on one of the sides is also approximately 882 N.