A container of weight W is suspended from ring A. Cable BAC passes through the ring and is attached to fixed supports at B and C. Two forces P = Pi and Q = Qk are applied to the ring to maintain the container in the position shown. Knowing that W = 376 N, determine P and Q. (Hint: The tension is

Question

A container of weight W is suspended from ring A. Cable BAC passes through the ring and is attached to fixed supports at B and C. Two forces P = Pi and Q = Qk are applied to the ring to maintain the container in the position shown. Knowing that W = 376 N, determine P and Q. (Hint: The tension is the same in both portions of cable BAC.)

Accepted Answer

[latex]\begin{aligned}\mathbf{T}_{A B} & =T \lambda_{A B} \& =T \frac{\overline{A B}}{A B} \& =T \frac{(-130 \mathrm{~mm}) \mathbf{i}+(400 \mathrm{~mm}) \mathbf{j}+(160 \mathrm{~mm}) \mathbf{k}}{450 \mathrm{~mm}} \& =T\left\lgroup-\frac{13}{45} \mathbf{i}+\frac{40}{45} \mathbf{j}+\frac{16}{45} \mathbf{k} ight group \\mathbf{T}_{A C} & =T \lambda_{A C} \& =T \frac{\overline{A C}}{A C} \& =T \frac{(-150 \mathrm{~mm}) \mathbf{i}+(400 \mathrm{~mm}) \mathbf{j}+(-240 \mathrm{~mm}) \mathbf{k}}{490 \mathrm{~mm}} \& =T\left\lgroup-\frac{15}{49} \mathbf{i}+\frac{40}{49} \mathbf{j}-\frac{24}{49} \mathbf{k} ight group \\Sigma F & =0: \quad \mathbf{T}_{A B}+\mathbf{T}_{A C}+\mathbf{Q}+\mathbf{P}+\mathbf{W}=0\end{aligned}[/latex]

Setting coefficients of i, j, k equal to zero:

[latex]\begin{array}{ll}\mathbf{i}:-\frac{13}{45} T-\frac{15}{49} T+P=0 & \qquad 0.59501 T=P &\qquad(1)\\\mathbf{j}: \quad+\frac{40}{45} T+\frac{40}{49} T-W=0 & \qquad 1.70521 T=W &\qquad(2)\\\mathbf{k}:+\frac{16}{45} T-\frac{24}{49} T+Q=0 & \qquad 0.134240 T=Q &\qquad (3)\end{array}[/latex]

Data:

[latex]\begin{aligned}& \qquad\qquad W=376 \mathrm{~N} \quad 1.70521 T=376 \mathrm{~N} \quad T=220.50 \mathrm{~N} \& 0.59501(220.50 \mathrm{~N})=P & P=131.2 \mathrm{~N} \blacktriangleleft\& 0.134240(220.50 \mathrm{~N})=Q & Q=29.6 \mathrm{~N}\blacktriangleleft\end{aligned}[/latex]

Question 2.123: A container of weight W is suspended from ring A. Cable BAC ...

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