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What vertical force is required to raise it? Neglect buoyancy force on gate.

A sliding gate 3m and 1.5m high situated in a vertical plane has a coefficient of friction between itself and guide of 0.18 if the gate weight is 19n and its upper edge is at a depth of 9m, what vertical force is required to raise it? Neglect buoyancy force on gate. -

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Width of the gate, b=3 m

Depth/Height of the gate, d=1.5m

Area of the gate, A=bxd=3x1.5=4.5m2

Weight of the gate 19KN

Coefficient of friction μ=0.18

Vertical force required to raise the gate:

Depth of c.g. of the gate from water surface,

ˉx=9+1.5/2=9.75m

Pressure force on the gate ,

P=wAˉx=9.81×4.5×9.75=430.4kN

Force required to raise the gate = frictional force+ weight of the gate

=μP+W=0.18×430.4+19=96.472kN.(ans)

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