A cube with 40-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/s^2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m^3.)

Question

Mathematics

Mcdaniel

10 August, 16:38

A cube with 40-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/s^2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m^3.)

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Teagan Schmidt · Answer 1

940.8 N

1254.4 N

Step-by-step explanation:

I would think the questions would be to calculate the forces at the top of the cube and at the sides. Thus:

On the top:

F = pressure * area

P = density * gravity * height

the height would be:

1m - 0.4m = 0.6m

replacing:

P = 1000 * 9.8 * 0.6 = 5880

A = (0.4) ^ 2 = 0.16

F = 5880 * 0.16

F = 940.8 N

On the sides:

dF = d * g * h * dA

dA = 0.4 * dh replacing

dF = 1000 * 9.8 * h * 0.4 * dh

dF = 3920 * h * dh

We integrate both sides and we have:

F = 3920 * (h ^ 2/2), h = 0.6 up to h = 1

F = (3920/2) * (1 ^ 2 - 0.6 ^ 2)

F = 1254.4 N