Hanging by a Thread

Abstract

Working in groups of four, decide on your roles first. Try to resolve questions within the group before asking for help. The " Secretary " is responsible for producing a final report and all parties are responsible for its content. The final report will consist of this page as a cover sheet as well as attached sheets that provide full explanations in complete sentences and display all relevant calculations in a clear and coherent manner. Turn in the final report at the beginning of the next class period. A 200 pound block is suspended from two cables that are attached at points A and B and joined to a ring at point C as shown in Figure 1. Distances are indicated in feet. Our first objective (see Problem 5) is to figure out the tension in the cables joining the ring to A and to B. 2 1 1 2 β α C B A Figure 1 Problem 1 Calculate the degree and radian measures of the angles α and β, as well as the indicated trigonometric values. Explain how you obtained your results on a separate sheet. Record the results of your calculations both here and on the separate sheet. deg rad sin cos tan α β There are three forces acting on the ring C. The weight of the block produces a tension force T W acting downward as in Figure 2. Tension in the cables produces forces T A and T B acting on the ring that are directed from the ring to the points A and B. The arrows in Figure 2 indicate the directions of these vectors, but are not drawn to scale. We know the magnitude of T W : 200 pounds. But we do not yet know the magnitude of the other two vectors.