Work and Energy in Pumping Water from a Trough

The video tutorial explains how to calculate the work required to empty a water-filled trough by pumping the water over the top. The trough is described as having a vertical cross-section shaped like the graph of y = x^2 from x = -1 to x = 1. The tutorial uses 62 pounds per cubic foot as the weight of water. It details the process of setting up the problem by determining small increments of work, calculating the force and volume of water layers, and using integration to find the total work required. The final calculation results in 198.4 foot-pounds of work needed to pump the water out of the trough.

What is the shape of the vertical cross-section of the trough?

• A rectangle

• A circle

• A triangle

• A parabola

What is the weight of water used in this problem?

• 80 pounds per cubic foot

• 70 pounds per cubic foot

• 62 pounds per cubic foot

• 50 pounds per cubic foot

What is the purpose of determining a small increment of work, Delta W sub 'i'?

• To calculate the total volume of water

• To find the total weight of the trough

• To compute the work needed to pump out one layer of water

• To measure the height of the trough

In the context of this problem, what does the force depend on?

• The height of the trough

• The weight of the water layer

• The speed of water flow

• The temperature of the water

How is the width of the water layer expressed as a function of y?

• y cubed

• y squared

• 2y

• 2 square root of y

What is the formula for the volume of the water layer?

• Length x Width

• Length x Height

• Width x Height

• Length x Width x Height

What is the integral used to calculate the total work?

• Integral from 0 to 1 of 62 x 12 y cubed

• Integral from 0 to 1 of 62 x 12 y squared

• Integral from 0 to 1 of 62 x 12 square root y

• Integral from 0 to 1 of 62 x 12 y

What is the final result of the work required to pump the water out of the trough?

• 175.3 foot-pounds

• 210.5 foot-pounds

• 198.4 foot-pounds

• 150.2 foot-pounds

What is the anti-derivative of y to the 1/2?

• y to the 2 divided by 2

• y to the 1/2 divided by 1/2

• y to the 5/2 divided by 5/2

• y to the 3/2 divided by 3/2

What is the distance the water must be pumped?

• 2 - y sub 'i'

• y sub 'i'

• 1 - y sub 'i'

• 1 + y sub 'i'