Two parallel, but not necessarily unidirectional, forces of magnitude 1 N and 2 N are acting on a body. Two more, parallel, again not necessarily unidirectional, forces of magnitude 3 N and 1 N, but perpendicular to the earlier forces, are applied to the body. Which one among the following are the smallest and largest possible magnitudes of the resultant force on the body?
√5 N and 5 N
The 1 N and 2 N forces act along one line, so depending on direction their combined effect ranges from |2-1| = 1 N to 2+1 = 3 N. Similarly, the 3 N and 1 N forces act along a perpendicular line, combining to between |3-1| = 2 N and 3+1 = 4 N. Since these two combined components are mutually perpendicular, the resultant ranges from a smallest of √(1²+2²) = √5 N to a largest of √(3²+4²) = 5 N.
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