The traffic light is mounted on a pole to which cable AB is connected. The tensi
ID: 2991832 • Letter: T
Question
The traffic light is mounted on a pole to which cable AB is connected. The tension in the cable is 400 N. (a) What is the moment (vector) about point C of the force that the cable exerts on point B? (b) What is the moment about the pole CD of the force that the cable exerts on point B?
The traffic light is mounted on a pole to which cable AB is connected. The tension in the cable is 400 N. (a) What is the moment (vector) about point C of the force that the cable exerts on point B? (b) What is the moment about the pole CD of the force that the cable exerts on point B?Explanation / Answer
(a) Length of AB = (82+42+12) = 9 m
Placing the origin at B, we get vector BA = -i - 8j + 4k
Hence unit vector in direction BA = -1/9 i - 8/9 j + 4/9 k
Hence, Force F can be written as -400/9 i - 400*8/9 j + 400*4/9 k
Vector CB is given by r = -i + 8j + 0*k
(a) Moment about C is given by rXF
M = ( -i + 8j + 0*k) X (-400/9 i - 400*8/9 j + 400*4/9 k)
M = (8*400*4/9 - 0*(-400*8/9)) i + (0*(-400/9) - (-1)(400*4/9)) j + ((-1)(-400*8/9) - 8*(-400/9)) k
M = 12800/9 i + 1600/9 j + 6400/9 k
(b) For moment of force about the pole, only z-direction component of force will act.
So, moment = (400*4/9)*1 = 1600/9 Nm
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.