MTH254-RecAct-Week1.pdf

# A 200 pound block is suspended from two cables that

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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. The objective in Problems 1-5 is to figure out the tension in the cables joining the ring to A and to B. We begin in Problem 1 by analyzing the geometry of the array. 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. Problem 2 Write a vector equation to express the fact that the ring is in equilibrium (no acceleration). Explain the principle(s) that justify your equation on a separate sheet. Write your equation on the separate sheet and in the box below.

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Math 254 Recitation Activity - Fall 2018 - Week 1 Page 4 of 4 Problem 3 In Figure 3 we have drawn the downward force ~ T W to scale and we have drawn the lines of action of the other two forces as dotted lines. The following
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