A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water. Assume that a = 4 m, b = 4 m, c = 6 m, and d = 1 m.)W =
Question
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water. Assume that a = 4 m, b = 4 m, c = 6 m, and d = 1 m.)W =
Solution
The work required to pump the water out of the spout can be calculated using the formula for work done, which is force times distance.
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First, we need to calculate the volume of the water in the tank. Since the tank is a rectangular prism, we can use the formula for the volume of a rectangular prism, which is length times width times height. In this case, a = 4 m, b = 4 m, and c = 6 m, so the volume V = a * b * c = 4 m * 4 m * 6 m = 96 m^3.
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Next, we need to calculate the weight of the water in the tank. The weight of an object is its mass times the acceleration due to gravity. The mass of the water is its volume times its density. In this case, the density of water is 1000 kg/m^3, so the mass M = V * density = 96 m^3 * 1000 kg/m^3 = 96000 kg. The acceleration due to gravity is 9.8 m/s^2, so the weight W = M * g = 96000 kg * 9.8 m/s^2 = 940800 N (Newtons).
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Finally, we need to calculate the work done to pump the water out of the spout. The work done is the force (which is the same as the weight in this case) times the distance. The distance is the height that the water needs to be pumped, which is d = 1 m. So the work done W = W * d = 940800 N * 1 m = 940800 J (Joules).
So, the work required to pump the water out of the spout is 940800 Joules.
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