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Question: 10 pts a simple control system allows liquid to be...

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(10 pts) A simple control system allows liquid to be dumped when its level rises sufficiently (Fig. 4). Specif- ically, a gate is hinged at point A and will open by ro- tating clockwise if D becomes large enough. Assuming the gate has a depth w into the paper, at what D will the gate just start to open if the liquid has a density ρ? Assume the vertical section is tall enough, such that the liquid does not spill over the top before the gate opens. Also, assume that the friction in the hinge and weight of the gate (and any moment imparted) are all small enough in this case to be neglected. Figure 4: Right angle gate.

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