A trough has a trapazoidal cross section with a height of 5 m and horizontal sid
ID: 2289137 • Letter: A
Question
A trough has a trapazoidal cross section with a height of 5 m and horizontal sides of width 2.5 m and 5m. Assume the length tof the trough is 13 m.
A trough has a trapazoidal cross section with a height of 5 m and horizontal sides of width 2.5 m and 5m. Assume the length tof the trough is 13 m. A trough has a trapezoidal cross section with a height of 5 m and horizontal sides of width 2-1/2 m and 5 m. Assume the length of the trough is 13 m. See the figure to the right. Complete parts a. and b. below. a. how much work is required to pump the water out of the trough (to the level of the top of the trough) when it is full? Use 1000 kg/m^3 for the density of water and 9.8 m/s^2 for the acceleration due to gravity. J (Type a whole number. Round to the nearest joule as needed.)Explanation / Answer
Volume of water inside this = Base area x Height
Base is trapezoid = 0.5 (2.5 + 5) * 5 = 18.75 m2
Height = 13 m
Volume = 13 * 18.75 = 243.75 m3
Total mass of water = desity * volume = 2.4375 x 105 kg
Work done to pump out the water = change in potential energy of system of water
Work = mg(H2 - H1)
H2 = initial position of centre of mass from ground
H1 = final position of centre of mass from ground
here H2 = 2.78 m (from bottom) (For trapezoid we have to memorize it)
H1 = 0
Work = 2.4375 x 105 * 9.8 * (2.78 - 0) = 6.64 x 106 J
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