Determine the Location of the Horizontal Axis $y _ { a }$

question 12

Multiple Choice

Determine the location of the horizontal axis $y _ { a }$ for figure (b) at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure (a) ) . The model for $y _ { a }$ is $y _ { a } = \bar { y } - \frac { I _ { y } } { h A }$ where $\bar { y }$ is the $y$ -coordinate of the centroid of the gate, $I _ { y }$ is the moment of inertia of the gate about the line $y = \bar { y } , h$ is the depth of the centroid below the surface, and $A$ is the area of the gate.

• A)\(y _ { a } = - \frac { a ^ { 2 } } { L }\)
• B)\(y _ { a } = - \frac { 4 a ^ { 2 } } { 3 L }\)
• C)\(y _ { a } = - \frac { a ^ { 2 } } { 4 L }\)
• D)\(y _ { a } = - \frac { 5 a ^ { 2 } } { L }\)
• E)\(y _ { a } = - \frac { a ^ { 2 } } { 3 L }\)

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Kinesthetic Sense

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The sensory modalities including touch, temperature, pain, and proprioception mediated by the skin's receptors.

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