A tank is full of water. Find the work required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3. (Assume a = 7 ft, b = 12 ft, and c = 14 ft.)
To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work.
The weight of the water can be found using the formula: weight = density * volume * gravity.
Given:
- Water density = 62.5 lb/ft^3
- Length (a) = 7 ft
- Width (b) = 12 ft
- Height (c) = 14 ft
First, calculate the volume of the tank using the formula: volume = length * width * height.
volume = 7 ft * 12 ft * 14 ft
= 1176 ft^3
Now, we can find the weight of the water using the formula: weight = density * volume * gravity.
weight = 62.5 lb/ft^3 * 1176 ft^3 * gravity (gravity is approximately 32.2 ft/s^2)
Calculate:
weight = 62.5 lb/ft^3 * 1176 ft^3 * 32.2 ft/s^2
Now, convert the weight into work by multiplying it by the distance the water needs to be pumped (assuming the spout is at the top of the tank).
work = weight * distance
Here, the distance is equal to the height of the tank, which is 14 ft.
work = (62.5 lb/ft^3 * 1176 ft^3 * 32.2 ft/s^2) * 14 ft
Finally, calculate the work required to pump the water out of the spout:
work = (62.5 lb/ft^3 * 1176 ft^3 * 32.2 ft/s^2) * 14 ft
To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank first. The weight of an object can be found by multiplying its volume by its density.
Given that the density of water is 62.5 lb/ft^3, and the dimensions of the tank are a = 7 ft, b = 12 ft, and c = 14 ft, we can calculate the volume of the tank:
Volume of the tank = a * b * c
Plugging in the values: Volume of the tank = 7 ft * 12 ft * 14 ft = 1,176 ft^3
Now, we can calculate the weight of the water in the tank using the formula:
Weight of water = Volume of water * Density of water
Weight of water = 1,176 ft^3 * (62.5 lb/ft^3) = 73,500 lb
Therefore, the work required to pump the water out of the spout would be equal to the weight of the water in the tank, which is 73,500 lb.