A spherical tank with 4 m radius is full of water. Calculate the work (in Joules) is needed to pump all of the water out if the water exits through a spout that is 2 meters from the top of the tank. The density of water is 1000kg/m3, the gravity force is 9.8m/s2.

Question

Physics

Amina Lowe

14 January, 17:50

A spherical tank with 4 m radius is full of water. Calculate the work (in Joules) is needed to pump all of the water out if the water exits through a spout that is 2 meters from the top of the tank. The density of water is 1000kg/m3, the gravity force is 9.8m/s2.

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Tristan Norman · Answer 1

1,075,536Joules

Explanation:

Work is said to be done when an applied force causes an object to cover a distance.

Workdone = Force * Distance

Before we can get the force needed to pump all the water out, we need to calculate the mass of water.

Density = Mass/volume

Mass = Density * volume

Given density of water = 1000kg/m³

Volume of the spherical tank = 4/3πr³

If radius = 4m

Volume of the tank = 4/3π (4) ³

= 4/3π * 64

= 27.16m³

Mass = 1000*27.16

Mass = 27,160kg

Force = mg = 27,160*9.8

Force = 537,768N

work (in Joules) needed to pump all of the water out if the water exits through a spout that is 2 meters from the top of the tank will be;

Work = 537,768*2

Work = 1,075,536Joules