Calculate the work (in joules) required to pump all of the water out of the tank. Assume that the tank is full, distances are measured in meters, and the density of water is 1,000 kg/m^3.
Water exits from a small hole at the top of the rectangular box. The dimensions are 8 m, 5 m, and 4 m.
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That's supposed to be a rectangular box, where the length is 8 m, the width is 4 m, and the height is 5 m.
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tigglebitties
To calculate the work required to pump all of the water out of the tank, we first need to calculate the volume of the water in the tank.
The volume of a rectangular box is calculated by multiplying its length, width, and height. In this case, the length is 8m, the width is 5m, and the height is 4m.
Volume = Length * Width * Height = 8m * 5m * 4m = 160m^3
Next, we need to calculate the mass of the water in the tank. The density of water is given as 1,000 kg/m^3.
Mass = Density * Volume = 1,000 kg/m^3 * 160m^3 = 160,000 kg
Now, we can calculate the work required to pump the water out of the tank. The work done in pumping a liquid is given by the equation:
Work = Force * Distance
In this case, the force required to pump the water out is equal to the weight of the water, which can be calculated using the formula:
Weight = Mass * Gravity
Assuming the acceleration due to gravity is 9.8 m/s^2, we have:
Weight = 160,000 kg * 9.8 m/s^2 = 1,568,000 N
Finally, to calculate the work, we need to multiply the weight by the height the water needs to be pumped. The water exits from a small hole at the top of the rectangular box, which is 5 meters above the base.
Work = Force * Distance = Weight * Height = 1,568,000 N * 5m = 7,840,000 Joules
Therefore, the work required to pump all of the water out of the tank is 7,840,000 Joules.