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Question

The traffic light shown in Figure is supported by a system of cables. Points A and B are in a vertical plane which is parallel to x-z plane. Point C is in y-z plane. The traffic light has a mass of 75 kg. Determine the following: (a). Position vectors for OA, OB and OC (b). Write equilibrium equations in the x, y and z directions (c). Find the tensions in cables OA, OB and OC (show all your workings that you do to find these) Image is at http://www.imagesup.net/?di=3135702364213 Question has been answered here: http://www.chegg.com/homework-help/questions-and-answers/the-access-door-is-held-in-the-200-open-position-by-the-cable-ab-as-shown-in-figure-5-the--q3496608 , but there is no explination or workings about how the answer for question a) was found? Also the image posted is very hard to read....

Solution

xxxxxxxxx of x = (x,-x,x) B =(x,-x,x) C =(x,x,x) x =(x,x,x)
(x) OA =(x-x)x -(x-x)x +(x-x)x = xx -8j +xx xx = 6i -xx +5k
xx = xx +5k
(b) xxx xxxxxxx xx cable x = xx                 =xx* unit xxxxxx in xx xxxxxxxxx                   =Ta (xx -8j +xx)/xxx
xxxxxxx in xxxxx B = xx*(xx -xx +5k)/105
xxxxxxx in xxxxx x =xx*(xx +5k)/89

x componet xx xxxxxxx = 4Ta/105 +xxx/xxx

y xxxxxxxxx xx xxxxxxx = -xxx/xxx -8Tb/105 +xxx/xx z xxxxxxxxx of xxxxxxx =5Ta/105 +xxx/xxx +xxx/xx xxxxxx of xxxxxx light = -xxx x

total xxxxx in x xxxxxxxxx = x xxxxxxxx of xxxxxxx = xxx/xxx +6Tb/105

xxxxx force xx y xxxxxxxxx =y xxxxxxxx of xxxxxxx = -xxx/xxx -8Tb/105 +xxx/xx

total xxxxx xx z direction = z xxxxxxxxx xx xxxxxxx + xxxxxx of xxxxxx xxxxx                                       =xxx/xxx +5Tb/105 +xxx/xx -xxx (x) total xxxxx in x xxxxxxxxx xx zero xxxxxxx there xx xx xxxxxx in x direction

xxxxx xxx/xxx +xxx/xxx =0

             xx =-xxx/x xxxxx force xx x xxxxxxxxx xx zxxx because xxxxx is xx xxxxxx xx y xxxxxxxxx

hence    -xxx/xxx -xxx/xxx +xxx/xx= 0

           or   -xxxx/xxx -xxx/xxx +xxx/xx=x

           xx    Tc = xxxxx/xxx xxxxx force xx x xxxxxxxxx xx zxxx because xxxxx is xx xxxxxx xx z xxxxxxxxx

hence xxx/xxx +xxx/xxx +xxx/xx -75g =x

           -x.xxx/xxx +xxx/xxx +xxxx/xxx-xxx = x

              xx.xxx = 75g105

                    xx = xxxxxx/xx.x =

                   xx =-xxx/x = -50g105/17.5

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The traffic light shown in Figure is supported by a system of cables. Points A and B are in a vertical plane which is parallel to x-z plane. Point C is in y-z plane. The traffic light has a mass of 75 kg. Determine the following: (a). Position vectors for OA, OB and OC (b). Write equilibrium equations in the x, y and z directions (c). Find the tensions in cables OA, OB and OC (show all your workings that you do to find these) Image is at http://www.imagesup.net/?di=3135702364213 Question has been answered here: http://www.chegg.com/homework-help/questions-and-answers/the-access-door-is-held-in-the-200-open-position-by-the-cable-ab-as-shown-in-figure-5-the--q3496608 , but there is no explination or workings about how the answer for question a) was found? Also the image posted is very hard to read....
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