Water Is Filled To A Height H 119 M Behind A Dam Of Width W 131 M See The Figure Determine The Resultant Force Exe 1 (65.27 KiB) Viewed 44 times
Water Is Filled To A Height H 119 M Behind A Dam Of Width W 131 M See The Figure Determine The Resultant Force Exe 2 (26.52 KiB) Viewed 44 times
Water is filled to a height H= 119 m behind a dam of width w = 131 m (see the figure). Determine the resultant force exerted by the water on the dam. SOLVE IT Conceptualize Because pressure varies with depth, we cannot calculate the force simply by multiplying the area by the pressure. Categorize Because of the variation of pressure with depth, we must use integration to solve this example, so we categorize it as an analysis problem. Analyze Let's imagine a vertical y axis, with y = 0 at the bottom of the dam. We divide the face of the dam into narrow horizontal strips at a distance y above the bottom, such as the red strip in the figure. The pressure on each such strip is due only to the water; atmospheric pressure acts on both sides of the dam. Use the equation to calculate the pressure due to the water at the depth h: Use the equation to find the force exerted on the shaded strip of area d4 = w dy: Integrate to find the total force on the dam (Use the following as necessary: p, w, H, and g): Substitute the known values to determine the total force acting on the dam. P= pgh = pg(H-y) dF = P dA= pg(H-y) w dy 0 Water exerts a force on a dam. P = - Pax = "09 ( sgw F= dA= pg (H-y) wdy H x N X 4
MASTER IT A glass with a square cross section when viewed directly from above is filled with water. The glass is 8.0 cm wide on each side and is 15.6 cm high. (a) Find the net horizontal force exerted by the water on each side. N (b) Find the net horizontal force exerted by the water on all four walls of the glass. N Find the net force exerted by the water on the bottom of the glass. N
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