Procedure for Analysis
Problems lhat involve the addition of lWO forces can be solved as
follows:
Parallelogram law.
• Two "componenl" forces Fl and F2 in Fig. 2- 106 add according to
the parallelogram law. yielding a re:m/lalll fo rce F Rt hat fonns the
diagonal of the paralle logram.
• If a force )- is to Ix: resolved into ('IJmfl(Jltl'lII$ along two axes 1/
and v, Fig. 2-IOb. Ihen start allhe head of force. F ,lnd construct
lines parallcl to Ihe axes. thereby forming Ihe paralleIOgr~ m . The
sides of the parallelogram represent the ,omponents. F~ and For
• Label ~11 the known ~nd unknown force magnitudes and the
angles on the sketch and identify the two unk nowns as Ihe
magnilude and direction of Fl!. or the magnitudes of its
components.
Trigonometry.
• Redraw a half portion of Ihe parallelogram 10 illustrate the
triangular head'lcrtaii addi tion of Ihe componenls.
• From Ihis triangle. the magnitude of the resuhant force can Ix:
determined using the law of cosines. and its dir.::clion is
determined from the law of sines. The magnitudes of two fo r,e
componentS arc determined from the law of sines. The formulas
arc given in Fig. 2- lIk