A flower pot is being held in an equilibrium position as shown in Figure using t

Question

A flower pot is being held in an equilibrium position as shown in Figure  using three cables OA, OB and OC. The weight of the flower pot is 300 N. Determine the following:

i.                    Position vectors for OA, OB and OC

ii.                  Write equilibrium equations in the x, y and z directions

iii.                Find the tensions in cables OA, OB and OC

A flower pot is being held in an equilibrium position as shown in Figure using three cables OA, OB and OC. The weight of the flower pot is 300 N. Determine the following: Position vectors for OA, OB and OC Write equilibrium equations in the x, y and z directions Find the tensions in cables OA, OB and OC

Explanation / Answer

i) OA = (8,0,0); OB =(-6,-5,5); OC =(0,8,5)

ii)

x-direction: T_oa-(6/root(86))*T_ob = 0 => T_oa - 0.647*T_ob = 0

y-direction: (-5/root(86))*T_ob+(8/root(89))*T_oc=0 => -0.539*T_ob + 0.848*T_oc = 0

z-direction: (5/root(86))*T_ob+(5/root(89))*T_oc=300 => 0.539*T_ob + 0.530*T_oc = 300

iii) tension in cables(solving ii)

T_oa = 221.6 N

T_ob = 342.5 N

T_oc = 217.7 N

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