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.
To calculate the work required to pump all the water out of the tank, you need to find the volume of water in the tank and then use the equation:
Work = Force × Distance
In this case, the force required is equal to the weight of the water, which can be calculated using the density of water.
Let's break down the steps:
1. Calculate the volume of water in the tank:
Volume = length × width × height
Volume = 8 m × 4 m × 5 m
Volume = 160 m^3
2. Calculate the weight of the water:
Weight = density × volume × acceleration due to gravity
Weight = 1,000 kg/m^3 × 160 m^3 × 9.8 m/s^2
Weight = 1,568,000 kg·m/s^2 (also known as a Newton, N)
3. Calculate the distance:
In this case, the distance is the height of the tank, 5 m.
4. Calculate the work:
Work = Force × Distance
Work = 1,568,000 N × 5 m
Work = 7,840,000 joules (J)
Therefore, the work required to pump all the water out of the tank is 7,840,000 joules (J).