By Irving H. Shames
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Extra resources for Engineering Machanics (Statics and Dynamics)
54. 59 relative to a reference xyz. The vector points away from the origin. 3, m = . I , and n = 9 5 for the xyz reference'? 55. What is the anglc bctwccn the I ,0011-N force and the axis A B ! The force is i n thc diagonal plane GCDE. 60. What is the rectangular component UC the 500-N forcc alirrig the diagonal Iron, R to A'! 60 ~ /I I\,l,lllllli. A radio tiiwci is held by guy wires. 61. 55 (iiven a force F = Ioi + sj Ak N. Xk, what shuuld A hc'! 56, + position, what is the angle brtwccn AH and U T !
In Fig. 8, the velocity vectors of three particles have equal length, are identically inclined toward the reference xyr, and havc the samc sense. Although they have different lines of actinn, they are nevertheless equal according to the definition. Two vectorr are equivalent in a certain c a p a c i y if each prodnces the vev ,same e f t k t in this capacity. If the criterion in Fig. 8is change of elevation of the particles or total distance traveled by the particles, all three vectors give the same result.
Other ways to use the reclangular parallelepiped. 20. Right triangle used fur sppecifying the direction ot it vector m two dirnensionq. There are times when the rectangular parallelpiped i s not shown explicitly. However. thc Icngth o f the sides o f one having the proper diagonal may hc availahle so that the replacement of the diagonal displacement vector into rectangular components can he readily achieved. The simplest procedure i s IO mcntally move from the beginning point o f the diagonal to the final point always moving along coordinatc directions, or, i n other words, always moving along the sides 0 1 the hypothetical rectangular parallelepiped.