A crane consists of a quarter-circular bar that lies in a plane parallel to the
ID: 2987325 • Letter: A
Question
A crane consists of a quarter-circular bar that lies in a plane parallel to the xz plane with a low-friction collar at point B that may side on a bar. THe forces supported by cables AB and BC are 30 lb and 1500 lb, respectively, and the coordinates of point A are given in the figure. For the value of angle? = 30.
Determine expressions for the forces the two cables apply to the collar at point B.
Explanation / Answer
You have to resolve B into a point (find its coordinates), which is easy enough to do. We already know that its Y component is 10 ft. Using trig, we can see that its x and z components are 5sin(30) and 5cos(30), respectively. Now that we have the point B, we can find vector BA by subtracting B from A. The next step, which seems to be getting left out, is that you have to find the unit vector of BA. To do this, divide each component by the vectors magnitude. It is imperative that this be done, as the vector of Fba = the magnitude of the force * the direction of the vector. It seems most people are simply multiplying the magnitude of the force by the vector itself. This is NOT correct.
Once you find the vector of Fba, we must find Fbc (which is simple enough). It is not necessary to resolve Fbc into its unit vector as we know its only component is in the negative z direction (unit vector is <0,-1,0>). Fbc = <0,-1500,0> lb.
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