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n open rectangular tank is filled to a depth of 2 m with water (density 1000 kg/m3). On top of the water there is a 1 m deep layer of gasoline (density 700 kg/m3). The width of the tank is 1 m (the direction perpendicular to the paper). The tank is surrounded by air at atmospheric pressure. Calculate the total force on the right wall of the tank, and specify its direction. The acceleration of gravity g = 9.81 m/s2.

Respuesta :

Answer:

gasoline zone    P_net = 6860 Pa

Water zone        P_net = 26460 Pa

Force direction is out of tank  

Explanation:

The pressure is defined

         P = F / A

         F = P A

let's write Newton's equation of force

            F_net = F_int - F_ext

            P_net A = (P_int - P_ext) A

             

The P_ext is the atmospheric pressure

         P_ext = P₀

the pressure inside is

gasoline zone

         P_int = P₀ + ρ' g h'

         

water zone

         P_int = P₀ + ρ' g h' + ρ_water h_water

     

we substitute

Zone with gasoline

            P_net = ρ' g h'

            P_net = 700 9.8  1

            P_net = 6860 Pa

Water zone

             P_net = rho’ g h’ + rho_water g h_water

             P_net = 6860 + 1000 9.8  2

             P_net = 26460 Pa

To find the explicit value of the force, divide by a specific area.

Force direction is out of tank

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