50 t t 32 example 7 a 100 lb weight hangs from two

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Unformatted text preview: sum of these forces. 50° 32° T¡ T™ EXAMPLE 7 A 100-lb weight hangs from two wires as shown in Figure 19. Find the tensions (forces) T1 and T2 in both wires and their magnitudes. SOLUTION We first express T1 and T2 in terms of their horizontal and vertical components. From Figure 20 we see that 100 5 6 FIGURE 19 T1 T2 The resultant T1 50° T¡ 32° T2 cos 32 i T1 sin 50 j T2 sin 32 j T2 of the tensions counterbalances the weight w and so we must have T™ 50° T1 cos 50 i 32° T1 T2 w 100 j Thus ( w T2 cos 32 ) i T1 cos 50 ( T2 sin 32 ) j T1 sin 50 100 j Equating components, we get T1 cos 50 T2 cos 32 0 T1 sin 50 FIGURE 20 T2 sin 32 100 Solving the first of these equations for T2 and substituting into the second, we get T1 cos 50 sin 32 cos 32 T1 sin 50 100 So the magnitudes of the tensions are T1 and T2 sin 50 100 tan 32 cos 50 T1 cos 50 cos 32 85.64 lb 64.91 lb Substituting these values in (5) and (6), we obtain the tension vectors T1 55.05 i 65.60 j T2 55.05 i 34.40 j 5E-13(pp 838-847) 1/18/06 11:14 AM Page 841 S ECTION 13.2 VECTORS |||| 13.2 The cost of a theater ticket The current in a river The initial flight path from Houston to Dallas The population of the world 9. A ■ vector 4, 7 ? Illustrate with a sketch. 3. Name all the equal vectors in the parallelogram shown. A B ■ 15. 0, 1, 2 , 1, ■ l (b) RP l (d) RS ■ B 3, 0 2, ■ ■ b i 4, 2j B 4, 2, 1 ■ ■ ■ ■ 5, 7 1, 0, 2 , ■ ■ ■ b, 2 a, and 3 a i 0, 4, 0 ■ ■ ■ ■ ■ ■ 4 b. 5j 1, 5, b b b ■ 1, 6, 2 1, k, 2 k, 3i ■ |||| ■ b 3, 2, 16. 3 b, a 3 j, 20. a 23–25 14. ■ 6, 2, 3 , ■ P ■ b 2i 22. a Q ■ 4, 3 , 21. a l PQ 0, 0, Find a , a |||| 19. a l PS l SP 2, 2 , 12. A 4, 0, 1 ■ 2, 4 ■ 18. a l QR l PS ■ 3, 17. a 4. Write each combination of vectors as a single vector. 10. A 3, 4 B 2, 3, ■ 13. 17–22 C B 13–16 |||| Find the sum of the given vectors and illustrate geometrically. ■ E D 1, 1, 11. A 0, 3, 1 , 2. What is the relationship between the point (4, 7) and the l (a) PQ l (c) QS 841 Exercises 1. Are th...
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This note was uploaded on 02/04/2010 for the course M 56435 taught by Professor Hamrick during the Fall '09 term at University of Texas at Austin.

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