Min force to open the water gate

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Homework Statement


why Fr(Lp) = FB / 2 ? can someone help to explain ?

Homework Equations

The Attempt at a Solution


shouldn't it be 2FB = Fr(Lp) ? since FB act on 2 sides of the gate ...[/B]
 

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It's Fb/2 because F acts at b/2 from the hinge. It only acts on one side.
Fr acts at Lp from the hinge on the other side.
 
Author sure has a funny way of drawing a 45 degree angle !
And conspicuously does not draw a hint of a hinge at B.

Furthermore, the horizontal line at 3 m is supposed to designate something sturdy that has water above and air below ? Quite something different from the liquid surface at 4.2 m; more like the stuff the gate itself should be made of. Deceptive drawing, incompetence, sloppiness ?