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p0144

# p0144 - 50 CHAPTER 1 INTRODUCTION 1.44 Chapter 1 Problem 44...

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50 CHAPTER 1. INTRODUCTION 1.44 Chapter 1, Problem 44 Problem: Two cables support an object of mass M . Express the cable tension forces, T AB and T BC , in vector form. The weight of the object in vector form is W = Mg k ,whe re g is the acceleration of gravity. Noting that the sum of these three forces is zero, determine the magnitude of the tension in each cable, T AB and T BC . Express your answers in terms of M , g , and the angle θ . •• M θ 90 o x z A B C g = g k ...................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .................................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solution: There are three forces acting at Point B as shown in the following figure. The vectors T AB and T BC are the cable-tension forces, and W = M g is the object’s weight. θ π / 2 θ T AB W T BC ..................................... . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................. . . . . . . . . . . . The cable-tension force vector for cable AB is T AB = T AB cos( π / 2 θ ) i + T AB sin( π / 2 θ ) k = T AB sin θ i + T AB cos θ k For cable BC, we have T BC = T BC cos θ i + T BC sin θ k Finally, the object’s weight vector is

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