The traffic light shown in Figure is supported by a system of cables. Points A a
ID: 1825643 • Letter: T
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....Explanation / Answer
cordinate of A = (4,-8,5)
B =(6,-8,5)
C =(0,8,5)
O =(0,0,0)
(a) OA =(4-0)i -(8-0)j +(5-0)k = 4i -8j +5k
OB = 6i -8j +5k
OC = 8j +5k
(b) let tension in cable A = Ta
=Ta* unit vector in OA direction
=Ta (4i -8j +5k)/105
tension in cable B = Tb*(6i -8j +5k)/105
tension in cable C =Tc*(8j +5k)/89
x componet of tension = 4Ta/105 +6Tb/105
y component of tension = -8Ta/105 -8Tb/105 +5Tc/89
z component of tension =5Ta/105 +5Tb/105 +5Tc/89
weight of trafic light = -75g k
total force in x direction = x componet of tension = 4Ta/105 +6Tb/105
total force in y direction =y componet of tension = -8Ta/105 -8Tb/105 +5Tc/89
total force in z direction = z component of tension + weight of trafic light
=5Ta/105 +5Tb/105 +5Tc/89 -75g
(c) total force in x direction is zero because there is no motion in x direction
hence 4Ta/105 +6Tb/105 =0
Ta =-3Tb/2
total force in x direction is zero because there is no motion in y direction
hence -8Ta/105 -8Tb/105 +5Tc/89= 0
or -12Tb/105 -8Tb/105 +5Tc/89=0
or Tc = 4Tb89/105
total force in x direction is zero because there is no motion in z direction
hence 5Ta/105 +5Tb/105 +5Tc/89 -75g =0
-7.5Tb/105 +5Tb/105 +20Tb/105-75g = 0
17.5Tb = 75g105
Tb = 75g105/17.5 =
Ta =-2Tb/3 = -50g105/17.5
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.