In Fig. 12-66. an 817 kg construction bucket is suspended by a cable A that is a
ID: 1477615 • Letter: I
Question
In Fig. 12-66. an 817 kg construction bucket is suspended by a cable A that is attached at 0 to two other cables B and C. making angles 01 = 51.0angle and 02 = 66.0 angle with the horizontal. To avoid solving two equations in two unknowns, position the axes as shown in the figure. Find the tensions in cable A, cable B, and cable C. Now rotate figure 12-66 90angle to the right (clockwise), and consider cable C to be a rod with mass 100 kg. Find the torque on rod C at the wall. Find the total compressive force on rod C. Assuming a cross sectional area of 50cm, what must the Young's modulus be to prevent a 2% deformation? Are you an engineering student? There is a name for this type of problem; what is it? These types of questions are essential to most engineering disciplines and engineering students will do a lot of them. Spend time developing a technique to take one through the procedure of solving these problems. Develop an acronym. For example C. D. A. S. (Cartoon, Diagram, Analyze, Substitute). Develop a prescription for how to represent summation of forces in vector form. Develop a list of questions to ask oneself that lead from the general model (For example: to the specifically relevant model. (Typically one separates the task of planning how the force vectors break down trigonometrically from finding the substitutions that express the force magnitudes themselves.)Explanation / Answer
1)
Let the Tension in Cable A = Ta
Let the Tension in Cable B = Tb
Let the Tension in Cable C = Tc
2)
Ta = 817 * 9.8 N
Ta = 8006.6 N
3)
Tb * cos(51) = Tc * cos(66)
Tb = Tc * cos(66)/cos(51)
Tb = Tc * 0.646
Tb * sin(51)+ Tc * sin(66) = 8006.6
Tc * 0.646 * sin(51)+ Tc * sin(66) = 8006.6
Tc * 1.416 = 8006.6
Tc = 5654.4 N
Tb = Tc * 0.646
Tb = 5654.4 * 0.646 N
Tb = 3652.75 N
Tension in Cable B, Tb = 3652.75 N
4)
Tension in Cable C, Tc = 5654.4 N