Work is the product of force and displacement. The amount of work needed to pump half of the water out of the aquarium is 4900 J.
What is work done?
Work done can be defined as the amount of force needed to displace an object from one location to another.
![W = F \cdot ds](/tpl/images/0025/7052/a7490.png)
Given to us
Volume of the aquarium, V = 4 x 1 x s = 4m³
Height of the aquarium, s = 1 m
Acceleration due to gravity, g = 9.8 m/s²
Density of water, ρ = 1000 kg/m³
We know about work done, it is given as,
![W = F \cdot ds](/tpl/images/0025/7052/a7490.png)
We also know that force can be written as,
![F = m \cdot a](/tpl/images/0025/7052/7db8f.png)
Also, the mass can be written as,
![m = \rho \times V](/tpl/images/0025/7052/b587f.png)
Therefore, work can be written as,
![W = F\cdot ds\\\\W = m \cdot a \cdot ds\\\\W = (\rho \times V \times a )ds\\\\W = \int (\rho \times V \times a )ds](/tpl/images/0025/7052/180e2.png)
As we need to pump half of the water, therefore, from below the tank to half the distance
![W = \int_0^{\frac{1}{2}} (\rho \times V \times a )ds\\\\W = \int_0^{\frac{1}{2}} (\rho \times (4 \times 1 \times s) \times a )ds\\\\W = (\rho \times 4 \times a )[s^2]_0^{\frac{1}{2}\\\\](/tpl/images/0025/7052/236ca.png)
Substitute all the values,
![W = 1000\times 4 \times g \times[(\dfrac{0.5}{2}^2) -0^2]\\\\W = 1000\times 4 \times 9.8 \times 0.125\\\\W = 4900\ J](/tpl/images/0025/7052/4c989.png)
Hence, the amount of work needed to pump half of the water out of the aquarium is 4900 J.
Learn more about Work:
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![An aquarium 4 m long, 1 m wide, and 1 m deep is full of water. find the work needed to pump half of](/tpl/images/0025/7052/29816.jpg)