A sculpture consisting of a 7.75lb metal rod with right-angle bends is to be hung against...

Transcribed Image Text:

A sculpture consisting of a 7.75lb metal rod with right-angle bends is to be hung against a vertical wall using a ball joint at O and two cables CD and AB as illustrated in figure 1. All straight parts of the rod are either horizontal or vertical. The center of mass of the rod is located at point E, where OE=(-1.75i + 0.036j + 2.1k)ft; the weight of the rod passes vertically through that point. Points B and D are located on the x-y plane. y DA CU a C 0.75' 1' 0.5' E OB 4.5' 2'- 10.5' 2.5' X Figure 1: The sculpture (shaded light red) is suspended by two cables CD and AB and attached to the wall at O via a ball joint. a) Draw a rigid body diagram of the sculpture. Indicate the reactions from the ball joint at O on your diagram. [5 pts] b) Write the expression for the vectors OA,OB, O, and OD. [2pts] c) Write a vector equation to show how the magnitude of the tension in cable AB (TAB) can be determined by analyzing the moments about the axis OC by determining the moment of TAB and the weight about the origin and resolving that moment along OC. Use Octave/MatLab to evaluate the TAB- [10pts] d) Similarly, write the vector equation showing how the length "a" can be found by analyzing the moments about the axis OD. Use your results from part c to evaluate "a". [10pts] e) Find the magnitude of the tension in cable CD (TCD) by taking moments about the origin. Use your results from parts c and d to evaluate TCD. [10pts] e) Find the reaction forces on the sculpture from its connection at O. [10pts] A sculpture consisting of a 7.75lb metal rod with right-angle bends is to be hung against a vertical wall using a ball joint at O and two cables CD and AB as illustrated in figure 1. All straight parts of the rod are either horizontal or vertical. The center of mass of the rod is located at point E, where OE=(-1.75i + 0.036j + 2.1k)ft; the weight of the rod passes vertically through that point. Points B and D are located on the x-y plane. y DA CU a C 0.75' 1' 0.5' E OB 4.5' 2'- 10.5' 2.5' X Figure 1: The sculpture (shaded light red) is suspended by two cables CD and AB and attached to the wall at O via a ball joint. a) Draw a rigid body diagram of the sculpture. Indicate the reactions from the ball joint at O on your diagram. [5 pts] b) Write the expression for the vectors OA,OB, O, and OD. [2pts] c) Write a vector equation to show how the magnitude of the tension in cable AB (TAB) can be determined by analyzing the moments about the axis OC by determining the moment of TAB and the weight about the origin and resolving that moment along OC. Use Octave/MatLab to evaluate the TAB- [10pts] d) Similarly, write the vector equation showing how the length "a" can be found by analyzing the moments about the axis OD. Use your results from part c to evaluate "a". [10pts] e) Find the magnitude of the tension in cable CD (TCD) by taking moments about the origin. Use your results from parts c and d to evaluate TCD. [10pts] e) Find the reaction forces on the sculpture from its connection at O. [10pts]