contestada

A swimming pool measures 5.0 m long x 4.0 m wide x 3.0 mdeep.
Compute the force exerted by the water against a) thebottom; b)
either end. (Hint: Calculate the force on athin,
horizontal strip at a depth h, and integratethis over the
end of the pool.) Do not include the force due to
airpressure.

Respuesta :

Answer:

a) 588,000 N

b) 294000 N

Explanation:

Given that

Density of water = 1000kg/m3

(g) = 9.8m/s2

volume is given as (V)= 5m*4m*3m

a) force will be equal to weight of water

[tex]W = mg  = \rho g V = 1000\times 9.8 \times (5*4*3) = 588,000 kg m/s^2[/tex]

b) at either end

[tex]P = \frac{F}{A} = P_o + \rho gh[/tex]

[tex]dF = PdA[/tex]

[tex]dF = \rho g w \int h dh[/tex]

[tex]F = \rho g w \frac{h^2}{2}[/tex]

[tex]F = \rho g A \frac{h}{2}[/tex]           [A = wh]

[tex]F = 1000\times 9.8 \times 5\times 4 \times\frac{3}{2}[/tex]

F = 294000 N