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=w\\displaystyle\\int_{a}^bxydy"

where

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

"y"  is the depth (in m) of the element of area

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

(for water, this is w  = 9800 N m-3)

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

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


We have:

"x=0.06\\ m"

"y"  is the variable of integration

"w=250000\\ N\/m^3"

"a=0"

"b=0.06"


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

"F=27N"



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS