An rectangular tank 5 m long, 2 m wide, and 8 m high is filled to a depth of 5 m of water. Set up the integral that would compute the work needed to pump the water out of a spout located at the top of the tank. Use the location of the origin and the direction of the positive axis as specified in the different parts. Note: Do not input values for the constant p9 (A) The origin is at the top of the tank with with positive y-values going down pg dy
(B) The origin is at the bottom of the tank with positive y-values going up. pg dy
(C) The origin is at the water level of the tank with positive y-values going down. dy

Solution:

Given data:

A rectangular tank with dimensions 5 m as length, wide of 2 m and height of 8 m is filled with water tot a depth of 5 m.

A). If we select an elemental part of the tank of thickness dy at a depth y from the top, its mass will be :

m = p.v

⇒ m = p.(Ady)

⇒ m = p.( 5 x 2 dy)

⇒ m = 10 p dy

Now work done in moving mass from a depth y to the top will,

dw = m.g.y

dw = (10 p dy).g.y

or dw = 10 p.g.y.dy

Total work done is :

W = 300 p.g

B). Origin at the bottom and consider an elemental part of the tank at a height y from the bottom, then its mass is :

⇒ m = p.( 5 x 2 dy)

⇒ m = 10 p dy

Now, work done in moving this mass from a height y above origin to a height 8 m above the origin is,

dw = mg(8 - y)

dw = (10 p dy).g.(8 - y)

dw = 10 pg.(8 - y). dy

The total work done is

W = 10 pg (40-12.5)

W = 275 pg

C). Origin at the water level and consider y axis positive in the downward direction.

The work done to move and elemental ,as from a depth y below the water level to the top of the tank is,

dw = 10 pg (y+2) dy

The total work done is :

W = 10 p g (12.5 + 10)

W = 225 pg

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

it is a negative acceleration