Question

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 17.6 cm high. (a) Find the net horizontal force exerted by the water on each side. (b) Find the net horizontal force exerted by the water on all four walls of the glass. (c) Find the net force exerted by the water on the bottom of the glass.

Answer 1

(a) The net force exerted by water on a vertical wall is given by :

F = PA

where P is the pressure at the mid point of wall.

A is the area of wall.

Thus P = gh where h = depth of mid point = 17.6/2 = 8.8 cm

Thus P = 1000*9.8* (8.8/100) = 862.4 Pa

A = 17.6*8 = 140.8 cm² = 0.01408 m²

     Thus Force F = 862.4 * 0.01408 = 12.142 N

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(b) The force exerted by water on opposite walls is equal in magnitude but opposite in direction.

Thus force exerted by water on all four walls cancel out each other.

Hence net horizontal force exerted by the water on all four walls of the glass = 0

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(c) Net force exerted on bottom = PA

where P = pressure at bottom

A = area of bottom

Thus Net force exerted on bottom = (1000*9.8*0.176)*(0.08*0.08) = 11.039 N