A block hangs from the end of bar AB that is 6.70 meters long and connected to t

Question

A block hangs from the end of bar AB that is 6.70 meters long and connected to the wall in the xzxz plane. The bar is supported at end A by a ball joint such that it carries only a compressive force along its axis. The bar is supported at end B by cables BD and BC that connect to the xz plane at points C and D respectively with coordinates given in the figure. The tension in cable BD is measured to be 283 Newtons.

Determine the equivalent force and couple system acting at A that models the forces exerted by both cables BD and BC on the bar at B. Enter your results for Feq and Meq in Cartesian Components.

Values for dimensions on the figure are given in the following table. Note the figure may not be to scale.

Variable Value

a 6.10 m

b 4.30 m

c 2.50 m

d 5.00 m

e 2.70 m

f 4.60 m

Explanation / Answer

givne length of the rod = l = 6.7 m

a = 6.1 m
b = 4.3 m
c = 2.5 m
d = 5 m
e = 2.7 m
f = 4.6 m

let tension in DB be T1, tension in CB be T2
then from force balance in vector notation
consider normal reaction at the point A be Rj ( where i j and k are unit vectors )

hence
T1((c - f)i + (0 - l)j + (d - e)k)/sqroot((c - f)^2 + (l^2) + (d - e)^2) + T2((a - f)i + (0 - l)j + (b - e)k)/sqroot((a - f)^2 + (l^2) + (b - e)^2) - mg k + R j = 0
T1(-0.284225i - 0.906814j + 0.311294 k) + T2(0.2127713i -0.9503785119j + 0.226956k) - mg k + R j = 0

now, T1 = 283 N
hence

(-80.435675i -256.628362j + 88.096202k) + T2(0.2127713i -0.9503785119j + 0.226956k) - mg k + R j = 0
comparing

T2 = 378.0381799 N
R = 615.907724 N
m = 17.72 kg

hence
Resultant force at A = 0 i + 615.907724j + 0k N
resultant moment at A = 0 Nm ( roller joints dont support moment)

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