A triangular-shaped gate is hinged at point A, as shown. Knowing that the weight of the gate is 100 N, determine the force needed to keep the gate at its position for unit width. The line of action of the weight of the gate is shown by the dashed line.
The force needed to keep the gate at its position for unit width.
Answer to Problem 85P
The force needed to keep the gate at its position for unit width is
Explanation of Solution
Given information:
The weight of the gate is
The below figure shows the force acting on the gate to keep it at equilibrium position.
Figure-(1)
Write the expression for Pythagoras theorem in triangle ABC.
Write the expression for hydrostatic force acting on the member
Here, the density of the water is
Write the expression for
Write the expression for hydrostatic force on member
Here, the location of Centroid of the member
Write the expression for point of application of force.
Here, the moment of inertia of the triangular gate is
Write the expression for area of the member
Here, the width of gate to be kept is
Write the expression for area of the member
Here, the width of gate to be kept is
Write the expression for the location of centroid of the member
Write the expression for moment of inertia of triangular gate.
Write the expression for moment about point
Here, the weight of the gate is
Calculation:
Substitute,
Substitute,
Substitute,
Substitute,
Substitute
Substitute
Substitute
Substitute,
Conclusion:
The force needed to keep the gate at its position for unit width is
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