Question
Asked Oct 11, 2019

The rod is supported by a ball-and-socket joint A and cables BC and BD. Suppose that F = 850 N . Determine the x, y, and z components of reaction at A necessary for equilibrium of the rod using scalar notation. Determine the tension in the cable BC necessary for equilibrium of the rod. Determine the tension in the cable BD necessary for equilibrium of the rod.

2m
2 m
о4
3 m
В
Е
х
3 m
3 m
у
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2m 2 m о4 3 m В Е х 3 m 3 m у

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Step 1

Refer to the provided diagram and draw the free body diagram of the rod. Here, Ax,, Ay and Az are the reaction forces at point A along x,y and z-direction respectively. Also, FBD and FBC are the tension forces in the cables BD and BC respectively.

ВС
Евt
BD
А,
В
850 N
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ВС Евt BD А, В 850 N

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Step 2

Refer to the provided diagram and write the co-ordinate points.

Coordinate point:
A(0,0,0)
B(6,0,0)
c(0.-2,3)
D (0,2,3)and
E(3,0.0)
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Coordinate point: A(0,0,0) B(6,0,0) c(0.-2,3) D (0,2,3)and E(3,0.0)

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Step 3

Next, writ the expression for the position vector of the cable BC (say, rBC) and plug the necessary values on the expression. Next, write the expression for the magnitude of the position vector of the cable BC (say, |rBC|) and plug the necessary values in the expression. Next,...

CC-B
(0-6)i(-2-0)j+(3-0)k
(-6i-2j+3k) m
ac=-6)+ (-2)+(3)
Piscl=
=7 m
Гвс
BC
BC
(-6i - 2j+3k) m
= F.
BC
7 m
2
-6
Faci
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CC-B (0-6)i(-2-0)j+(3-0)k (-6i-2j+3k) m ac=-6)+ (-2)+(3) Piscl= =7 m Гвс BC BC (-6i - 2j+3k) m = F. BC 7 m 2 -6 Faci

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