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 large helium-filled caricature balloon featured in a local parade is steadied by two ropes tied to its midpoint. One rope extending on one side of the balloon is inclined at 20° to the vertical. A second rope located on the other side of the balloon is inclined at 30° to the vertical. If the balloon has a buoyancy of 200 kN, what will be the tension in each of the ropes?
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