Undergrad Question about Hydrostatic Force?

[Virang807]

Hello! I am currently in Calculus 2 and we are dealing with hydrostatic force. I get the integration that happens but I always seem to have trouble with solving the word problems. With this problem, I realize that I use integrate by making an infinite number of rectangles on the 2 triangles. I want to know the differences in solving both of them and trying to find the width formula with respect to x. Thank you!

 

[SteamKing]

Hello! I am currently in Calculus 2 and we are dealing with hydrostatic force. I get the integration that happens but I always seem to have trouble with solving the word problems. With this problem, I realize that I use integrate by making an infinite number of rectangles on the 2 triangles. I want to know the differences in solving both of them and trying to find the width formula with respect to x. Thank you!

There are no substantial differences in solving these problems; the regions are slightly different is all. If you can solve for the hydrostatic force on one triangle, you can solve for the force on the other.

The key here is you know that both triangles are equilateral, so you can figure their altitudes. What you want to do is set up a relation between the depth of the triangle below the attachment point and the width of the triangle at that depth.