Answer to Question #108763 in Calculus for Edward

Question #108763
Find the force on one side of a cubical container 6.0 cm on an edge if the container is filled with
mercury. The weight density of mercury is 250 kN/m³.
1
Expert's answer
2020-04-10T17:11:15-0400

The total force on the plate is given by


F=wabxydyF=w\displaystyle\int_{a}^bxydy

where

xx  is the length (in m) of the element of area (expressed in terms of y)

yy  is the depth (in m) of the element of area

ww  is the density of the liquid (in N m-3)

(for water, this is w  = 9800 N m-3)

aa  is the depth at the top of the area in question (in m)

bb  is the depth at the bottom of the area in question (in m)


We have:

x=0.06 mx=0.06\ m

yy  is the variable of integration

w=250000 N/m3w=250000\ N/m^3

a=0a=0

b=0.06b=0.06


F=25000000.060.06ydy=15000[y22]0.060=27(N)F=250000\displaystyle\int_{0}^{0.06}0.06ydy=15000\bigg[{y^2\over2}\bigg]\begin{matrix} 0.06 \\ 0 \end{matrix}=27(N)

F=27NF=27N



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