Physics horizontal force by water?

Question

A dam is 32 m high and 600 m wide. Claculate the total horizontal force (in Newton) exerted on the dam by the water on the dam is nearly:

a) 6 x 10 to the sixth b) 3 x 10 to the sixth

c) 6 x 10 to the ninth d) 3 x 10 to the ninth

Answer 1

How you solve this depends on whether you're expected to know calculus.

With calculus, the force is the integral of pressure times area:

F = ∫ P • dA = &int P dx dy (since the pressure is in the direction of area).

The pressure doesn't depend on the x position, just the depth y, so if the width is w:

F = w ∫ P dy

P = ρgy where y is zero at the top of the dam and down is positive y.  You should be able to do the rest from there.

Without calculus, find the pressure at the bottom, and assume it increases linearly, so the total is one half max pressure times total area.  :)