The uniform control gate A B is pinned at A and rests on the smooth surface at B The gate has a mass of 8 5 0 0 kg and has a width of 1 m Answer the following questions 1 5 points a Determine the resultant force exerted by water on the control gate b Determine the maximum depth of water h in the reservoir that will cause the gate to be on the verge of opening c Optional Extra Credit, 3 points Determine the location of the resultant force measured from A Useful information 1 0 0 0 k g m 3 , g 9 8 1 m s 2 The increase in pressure with depth h for a confined fluid is given by h or g h The area of a trapezoid shown in the figure is ( a b ) h 2 and the coordinate of the centroid measured from location O is h 2 , ( a 2 b ) h 3 ( a b ) 6

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Question: The uniform control gate A B is pinned at A and rests on the smooth surface at B . The gate has a mass of

The uniform control gate

A B

is pinned at A and rests

on the smooth surface at

B .

The gate has a mass of

8500

kg and has a width of

1

.

Answer the following

questions:

[15

points

]

.

Determine the resultant force exerted by water on

the control gate.

.

Determine the maximum depth of water

h

in the

reservoir that will cause the gate to be on the verge

of opening.

. [

Optional Extra Credit,

3

points

]

Determine the

location of the resultant force measured from

A .

Useful information:

= 1000 k \frac{g}{m^{3}}, g = 9.81 \frac{m}{s^{2}} .

The increase in

pressure with depth

h

for a confined fluid is given by

h

g h .

The area

of a trapezoid shown in the figure is

\frac{(a + b) h}{2}

and the coordinate of the

centroid measured from location O is

[\frac{h}{2}, \frac{(a + 2 b) h}{3 (a + b)}] *_{6}

The uniform control gate A B is pinned at A and

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