Question

Calculate the work in megajoules (1 MJ=1×10⁶ J) required to pump all the water out of a full trough from which water exits by pouring over the sides. An illustration shows an inverted trapezoidal trough with base widths of a on bottom and b on top, a height h, and length c. Assume that =10 m, =13 m, c=9 m, and ℎ=2 m. The density of water is 1000 kg/m³, and =9.8 m/s². (Use decimal notation. Give your answer to two decimal places.)

Answer 1

First, calculate the volume and mass of the water. Then, calculate the work required using gravitational potential energy. The work required to pump out all the water is approximately 4057.20 megajoules.

The task is to calculate the work required to pump the water out of a trapezoidal trough. Firstly, we need to calculate the volume of the trapezoid in order to obtain the mass of water. The formula is given as V = (a + b)/2 * h * c.

Then, substituting the given values: V = (10 + 13)/2 * 2 * 9, we get V = 207 cubic meters. To find the mass of the water, we multiply the volume by the density of water (1000 kg/m3). Hence, m = 207,000 kg.

Then, knowing that the work (W) needed to pump the water out is calculated as the gravitational potential energy, we use the equation W = mgh. So, W = 207,000 * 9.8 * 2 gives us W = 4,057,200,000 J. To convert to megajoules, we divide by 1x10^6, yielding W = 4057.2 MJ.

So, it would require approximately 4057.20 megajoules to pump all the water out of the full trapezoid trough.