The following four problems involve vector addition. Vector manipulation is an important skill for estimating forces in mechanical systems. When adding forces or other quantities represented as vectors, the principles of vector addition must be followed. Vectors to be added are first decomposed into their respectivex, y, and z components. These components are added together separately, then recombined to form the total resultant vector. Sometimes, it’s convenient to decompose vectors into components lying on axes other than rectilinear x-,y-,and z-axes.
A guy wire exerts a force on an eye bolt that is screwed into a wooden roof angled at 30° to the horizontal. The guy wire is inclined at 40° to the horizontal. If the eye bolt is rated at a maximum force of 1000 N perpendicular to the roof, how much tension can safely be applied to the guy wire?
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