Question

A 12m long gate that is 4 m wide is placed against a body of water at an angle of 60 degrees. The gate is being pulled by a rope placed 3 m from the top of the gate at 60 kN. If the water is 9 m deep, what is the minimum weight of the gate that will cause it to rotate clockwise

Answer 1

Since the weight cannot take a negative value, it is concluded that the minimum weight required for the gate is zero, because the same pressure force will rotate the gate.

Step-by-step explanation:

Given:

L = 12 m

F = 60 kN

w = 4 m

H = 9 m

The pressure force is:

`F_(p) =\rho gAx=1000*9.8*(9)/(sin60) *4*(9)/(2) =1833.203kN`

The center of pressure is:

`h=((((9)/(sin60))^(3) *4 )/(12)*sin^(2)60 )/((9)/(sin60)*4*(9)/(2) ) +(9)/(2) =6`

If the moment is equal to zero,

`F_(p) *(9-6)+W*(L)/(2) cos60=F*9\\1833.203*3+W*6*cos60=60*9\\W=-1653.2kN`