Question

A cube with 45-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. (b) Estimate the hydrostatic force on one of the sides of the cube.

Answer 1

1) Force on top face
`=1.09kN`

2)Force on the side face
`=1.539kN`

Step-by-step explanation:

a)

We know that

`Force=Pressure* Area`

Pressure shall be calculated at a depth of (1-0.45) meters from the top of the water surface

`Pressure=\rho * g* h\\\\\therefore Pressure=1000* 9.81* (1-0.45)Pa\\\\Pressure=5.395kPa`

Thus force is calculated as under

`Force=5.395* (0.45)^(2)\\\\Force=1.09kN`

b)

The force on one of it's sides is calculated in the same manner except that the pressure is obtained at the centroidal level of the face of cube

Thus

`Force=\rho * g* h_(cg)* Area\\\\Force=1000* 9.81* (1-(0.45)/(2))* (0.45)^(2)\\\\Force=1.539kN`