A swimming pool has dimensions 32.0 m x 12.0 m and a flat bottom. The pool is filled to a depth of 2.30 m with fresh water. (a) What is the force exerted by the water on the bottom? 8.65E6 was right but B and C are wrong
(b) What is the force exerted by the water on each end? (The ends are 12.0 m.) i got 311 but its wrong
(c) What is the force exerted by the water on each side? (The sides are 32.0 m.) and 829 was also wrong
(a) As we know that static water pressure is the same in all direction.
Also, the hydrostatic pressure at a given height is represented by the formula -
P = ρ x g x h.
This means, at 'h' meters from the surface the pressure is the
same in all directions. This is also called pascal's
rule.
Also,
Force = Pressure x Area.
Therefore, pressure exerted by the water on the bottom (at point
2.30 m) = 1000 x 9.80 x 2.30
= 22540 Pa
Area = 32.0 x 12.0 = 384 m^2
So, force exerted on the floor = Pressure x Area = 22540 x 384 =
8655360 N = 8.65 x 10^6 N
(b) Area of one side = 2.30 x 12.0 = 27.6 m^2
So, force exerted on the side = 22540 x 27.6 = 622104 N
(c) Area of other side = 32.0 x 2.30 = 73.6 m^2.
Therefore, total force exerted on that side = 22540 x 73.6 =
1658944 N
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