A water trough has a semicircular cross section with a radius of 0.3 m and a length of 1 m (see figure). a. How much work is required to pump the water out of the trough (to the level at the top of the trough) when it is full? Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. b. If the length is doubled, is the required work doubled? Explain. c. If the radius is doubled, is the required work doubled? Explain. 1 m 0.3 m
A water trough has a semicircular cross section with a radius of 0.3 m and a length of 1 m (see figure). a. How much work is required to pump the water out of the trough (to the level at the top of the trough) when it is full? Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. b. If the length is doubled, is the required work doubled? Explain. c. If the radius is doubled, is the required work doubled? Explain. 1 m 0.3 m
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Transcribed Image Text:A water trough has a semicircular cross section with a radius of 0.3 m and a length of 1 m (see figure).
a. How much work is required to pump the water out of the trough (to the level at the top of the trough) when it is full? Use 1000 kg/m³ for
the density of water and 9.8 m/s² for the acceleration due to gravity.
b. If the length is doubled, is the required work doubled? Explain.
c. If the radius is doubled, is the required work doubled? Explain.
1 m
0.3 m
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VIEWStep 2: Draw a diagram of the situation:
VIEWStep 3: Write the expression for the change in the potential energy of the element:
VIEWStep 4: Find the expression for the work required to pump the liquid out of container:
VIEWStep 5: (a) Calculate the work required to be done on liquid:
VIEWStep 6: (b) Know what happens when the length of the container is doubled:
VIEWStep 7: (c) Know what happens when the radius of the container is doubled:
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