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.
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 of the water out of the tank, we need to find the volume of water in the tank and then multiply it by the weight of the water.
1. Find the volume of water in the tank:
Volume = length x width x height
Volume = 8 m x 4 m x 5 m
Volume = 160 m^3
2. Convert the volume to kilograms:
Mass = Volume x Density
Mass = 160 m^3 x 1,000 kg/m^3
Mass = 160,000 kg
3. Calculate the weight of the water:
Weight = Mass x Gravitational acceleration
Gravitational acceleration is typically 9.8 m/s^2
Weight = 160,000 kg x 9.8 m/s^2
Weight = 1,568,000 N (Newtons)
4. Calculate the work done:
Work = Force x Distance
Since the water is being pumped straight up, the distance is the height of the tank, which is 5 m.
Work = 1,568,000 N x 5 m
Work = 7,840,000 joules
Therefore, the work required to pump all of the water out of the tank is 7,840,000 joules.