Question

A rectangular tub with dimensions width 4 feet, depth 7 fect and height 10 feet is full of a liquid that weighs about 3 pounds per square foot. Compute how much work it would take to pump half of the liquid out of the top of the tank. As always. be sure to include appropriate units.

Answer 1

Step-by-step explanation:

To compute the work required to pump half of the liquid out of the tub, we need to calculate the weight of the liquid and then multiply it by the height it needs to be lifted.

First, let's calculate the weight of the liquid in the tub. The density of the liquid is given as 3 pounds per square foot. The area of the tub's base can be found by multiplying the width by the depth:

Area = width * depth = 4 ft * 7 ft = 28 square feet

The weight of the liquid in the tub is then given by:

Weight = density * area = 3 lb/ft^2 * 28 ft^2 = 84 pounds

Since we are pumping out half of the liquid, we need to calculate the weight of half the liquid:

Weight of half the liquid = 84 pounds / 2 = 42 pounds

Now, we can calculate the work required to lift this weight to the top of the tank, which has a height of 10 feet:

Work = weight * height = 42 pounds * 10 feet = 420 foot-pounds

Therefore, it would take approximately 420 foot-pounds of work to pump half of the liquid out of the top of the tank.