- #1
kudoushinichi88
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Homework Statement
A uniform rectangular plate of width d, height h, and weight W is supported with its top and bottom edges horizontal. At the lower left corner there is a inge, and the upper right corner there is a cable. For what angle [itex]\theta[/itex] with the vertical will the tension in the cable be the least, and what is the tension?
Homework Equations
[itex]\tau=Fd[/itex]
The Attempt at a Solution
for the angle, it's easy,
[itex]tan \theta = d/h[/itex]
[itex]\theta=\arctan{d/h}[/itex]
but I'm having trouble with the tension of the cable. I managed to derive
[itex] \frac{Wd}{2}=Td\cos{\theta}+Th\sin{\theta}[/itex]
which gives T as
[itex]T=\frac{Wd}{2\left(d\cos{\theta}+h\sin{\theta})}[/itex]
the answer given is
[itex]T=(Wd/2)\sqrt{h^2+d^2}[/itex]
I seem to fail to see the connection
[itex]\sqrt{h^2+d^2}=\frac{1}{d\cos{\theta}+h\sin{\theta}}[/itex]
can anyone show me why is this so?
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