<h2>
Answer: 4900 J</h2>
Explanation:
Let's begin by explaining that the Work done by a Force refers to the release of potential energy from a body that is moved by the application of that force to overcome a resistance along a distance . When the applied force is constant and the direction of the force and the direction of the movement are parallel, the equation to calculate it is:
(1)
In the case of this rectangular aquarium (see figure attached), we know its initial volume (which is the same volume occupied by water, because the tank is full) is:
(2)
In addition, we know the force needed to pump a small amount of water is:
(3)
On the other hand, we know the density of the water is given by the following equation:
(4)
Where is the mass of water and is the <em>volume of a thin "sheet" of water.</em>
Finding :
(5)
Substituting (5) in (3):
(6)
And substituting (6) in (1):
(7)
Now, we are asked to find the work needed to pump half of the water out of the aquarium. So, if the aquarium is deep, the half is :
(8)
(9)
Well, in order to solve this, we have to write the definite integral from y=0 mto y=0.5m:
(10)
Knowing :
(11)
(12)
>>>>This is the work needed to pump half of the water out of the aquarium