A load is suspended from the bar OA by a cable, as shown....

A load is suspended from the bar OA by a cable, as shown. The suspended load exerts a downward force F = 600-lb on the bar at A. The bar has negligible weight and is supported by a ball-and-socket joint at O and by two wall-mounted cables AB and AC. A colleague analyzes this system and concludes that the cable tensions must be TAB = 474.1-lb and TAC = 247.9-lb, in order to maintain equilibrium. Further, she reports that the associated reaction force at O must be R = 541.9î + 406.5? + 0? (lb). Determine whether or not your colleague's analysis is correct. Justify your response. C (0, 6, -10) ft A (8, 6, 0) ft B (0, 10, 4) ft -Fj

Transcript

00:01 A load is suspended from the bar o a by the cable shown the suspended load exerts a downward force f equals six hundred l b on bar at a point the bar has the negligible weight and is supported by the ball and socket joint at o and by two wall mounted cables ab and a c a colleague analyst an analyzes the system and concludes that the cable tensions tab is 474 .1 lv and tension is ac is 247 .9 lb.

00:46 In order to maintain the equilibrium further reported that associated reaction force reaction force at o must be r equals 541 .9 i cap plus 406 .5 j cap plus zero cap lb.

01:12 Then determine whether or not the colleague's analysis is right.

01:19 We have given with the coordinates of a, b and c, we have to find the position vector.

01:26 Ab is equal to 0 minus 8 i cap plus 10 minus 6 j cap plus 4 minus 0 k cap then a b vector will be equals to minus 8 i plus 4 j plus 4k and the magnitude or the unit vector for this is equal to vector divided by the magnitude which will be equals to minus 8 i plus 4 j plus 4k divided by root of minus 8 whole square plus 4 square plus 4 square plus 4 square the unit vector ab will be equals to minus 8 i plus 4 j plus 4k divided by 9 .8 now finding the ac vector is equal to 0 minus 8 i plus 6 minus 6 j plus minus 10 minus 0 k cap then ac vector will be minus 8 i minus 10 k finding the unit vector for this is equals to ac vector divided by its magnitude is equal to minus 8 i minus 10 k divided by root of minus 8 whole square plus minus 10 whole square this will be equal to to minus 8i minus 10k divided by 12 .8.

03:05 Then the resultant is negative of the resultant vector is equals to tension in ab multiplied by the unit vector of ab plus tension in ac into unit vector ac minus fj force...

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