3-38 The traffie light shown in Fig P3-39 is supporled bya sysieut oi cables Delermine the teneiuns a: cables A. 8.arnd Cit the taffic light has a mass of I00 kg.

Given: Weight of the traffic light, W=100 kg=100×10=1000 N=1 kN The force vector of the strings are…

Answered: 3-38 The traffie light shown in Fig…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

3-38 The traffie light shown in Fig P3-39 is supporled by
a sysieut oi cables Delermine the teneiuns a: cables A. 8.
arnd Cit the taffic light has a mass of I00 kg.

Expert Solution

Step 1

Given:

$\begin{array}{ccl} Weight of the traffic light, W & = & 100 kg \\ = & 100 \times 10 \\ = & 1000 N \\ = & 1 kN \end{array}$

The force vector of the strings are given as the,

$\begin{array}{ccl} O A & = & 4 i - 8 j + 5 k \\ O B & = & - 6 i - 8 j + 5 k \\ O C & = & 8 j + 5 k \end{array}$

Step 2

The tension vector in the strings can be written as the,

$\begin{array}{ccl} T_{O A} & = & T_{O A} \frac{O A}{|O A|} \\ = & T_{O A} \frac{4 i - 8 j + 5 k}{\sqrt{4^{2} + {(- 8)}^{2} + 5^{2}}} \\ = & T_{O A} (0.39 i - 0.78 j + 0.48 k) \end{array}$

Similarly,

$\begin{array}{ccl} T_{O B} & = & T_{O B} \frac{O B}{|O B|} \\ = & T_{O B} \frac{- 6 i - 8 j + 5 k}{\sqrt{- 6^{2} + {(- 8)}^{2} + 5^{2}}} \\ = & T_{O B} (0.36 i - 0.72 j + 0.44 k) \\ \begin{array}{c} \end{array} \end{array}$

$\begin{array}{ccl} T_{O C} & = & T_{O C} \frac{O C}{|O C|} \\ = & T_{O C} \frac{8 j + 5 k}{\sqrt{{(8)}^{2} + 5^{2}}} \\ = & T_{O C} (0.847 j + 0.53 k) \end{array}$