Find the work done in pumping gasoline that weighs 6600 newtons per cubic meter. A cylindrical gasoline tank 3 meters in diameter and 6 mete

Question

Find the work done in pumping gasoline that weighs 6600 newtons per cubic meter. A cylindrical gasoline tank 3 meters in diameter and 6 meters long is carried on the back of a truck and is used to fuel tractors. The axis of the tank is horizontal. The opening on the tractor tank is 5 meters above the top of the tank in the truck. Find the work done in pumping the entire contents of the fuel tank into the tractor.

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Helga 4 years 2021-08-15T08:40:50+00:00 1 Answers 33 views 0

Answers ( )

  1. binhan
    0
    2021-08-15T08:42:36+00:00
    Reply

    Answer:

    work done in pumping the entire fuel is 1399761 J

    Explanation:

    weight per volume of the gasoline = 6600 N/m^3

    diameter of the tank = 3 m

    length of the tank = 6 m

    The height of the tractor tank above the top of the tank = 5 m

    The total volume of the fuel is gotten below

    we know that the tank is cylindrical.

    we assume that the fuel completely fills the tank.

    therefore, the volume of a cylinder =  

    where r = radius = diameter ÷ 2 = 3/2 = 1.5 m

    volume of the cylinder = 3.142 x  x 6 = 42.417 m^3

    we then proceed to find the total weight of the fuel in Newton

    total weight = (weight per volume) x volume

    total weight = 6600 x 42.417 = 279952.2 N

    therefore,

    the work done to pump the fuel through to the 5 m height = (total weight of the fuel) x (height through which the fuel is pumped)

    work done in pumping = 279952.2 x 5 = 1399761 J

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