Answered: -d- A 100 mm 90 N 90 N B. -100 mm→<100…

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

A rod AB, hinged at A and attached at B to cable BD , supports the loads shown. Knowing that d = 150 mm, determine (a) the tension in cable BD, (b) the reaction at A.

-d-
A
100 mm
90 N
90 N
B.
-100 mm→<100 mm-
→-
+100 mm

Expert Solution

Step 1

Given data:

The distance between point A and D, d = 150 mm.

Draw the free-body diagram of the system.

Step 2

Calculate the angle made by cable with horizontal.

$\begin{array}{rcl} θ & = & 90 ° - \tan^{- 1} (\frac{300 mm \times \frac{1 m}{1000 mm} - 150 mm \times \frac{1 m}{1000 mm}}{100 mm \times \frac{1 m}{1000 mm}}) \\ = & 33.7 ° \end{array}$

Apply the moment of equilibrium at point A.

$\begin{array}{rcl} Σ M_{A} & = & 0 \\ [(90 N \times 0.1 m \times) + (90 N \times 0.2 m) + (F_{D B} \cos 33.7 ° \times 0.1 m \times) - (F_{D B} \sin 33.7 ° \times 0.3 m)] & = & 0 \\ 9 N \cdot m + 18 N \cdot m & = & F_{D B} (0.083 m) \\ 27 N \cdot m & = & F_{D B} (0.083 m) \\ F_{D B} & = & 325.30 N \end{array}$

Hence, the tension in the cable is 345.30 N.

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