A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30° angles with the vertical. Knowing that the x component of the force exerted by wire AD on the plate is 110.3 N, determine (a) the tension in wire AD, (b) the angles θx, θy, and θz

Question

A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30° angles with the vertical. Knowing that the x component of the force exerted by wire AD on the plate is 110.3 N, determine (a) the tension in wire AD, (b) the angles [latex]{ heta }_{ x }[/latex], [latex]{ heta }_{ y }[/latex], and [latex]{ heta }_{ z }[/latex] that the force exerted at A forms with the coordinate axes.

Accepted Answer

[latex]\begin{aligned}(a)\qquad & F_{x}=F \sin 30^{\circ} \sin 50^{\circ}=110.3 \mathrm{~N} \quad \text { (Given) } \& F=\frac{110.3 \mathrm{~N}}{\sin 30^{\circ} \sin 50^{\circ}}=287.97 \mathrm{~N} & F=288 \mathrm{~N}\blacktriangleleft \\(b)\qquad & \cos \theta_{x}=\frac{F_{x}}{F}=\frac{110.3 \mathrm{~N}}{287.97 \mathrm{~N}}=0.38303 & \theta_{x}=67.5^{\circ} \blacktriangleleft\\& F_{y}=F \cos 30^{\circ}=249.39 \& \cos \theta_{y}=\frac{F_{y}}{F}=\frac{249.39 \mathrm{~N}}{287.97 \mathrm{~N}}=0.86603 & \theta_{y}=30.0^{\circ}\blacktriangleleft \\& F_{z}=-F \sin 30^{\circ} \cos 50^{\circ} \& \quad =-(287.97 \mathrm{~N}) \sin 30^{\circ} \cos 50^{\circ} \& \quad =-92.552 \mathrm{~N} \\& \cos \theta_{z}=\frac{F_{z}}{F}=\frac{-92.552 \mathrm{~N}}{287.97 \mathrm{~N}}=-0.32139 & \theta_{z}=108.7^{\circ}\blacktriangleleft\end{aligned}[/latex]

Question 2.133: A horizontal circular plate is suspended as shown from three...

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