Chapter 377*P3.66Let θrepresent the angle the x-axis makes with the horizontal. Sinceangles are equal if their sides are perpendicular right side to rightside and left side to left side, θis also the angle between the weightand our yaxis. The x-components of the forces must add to zero:−+=0 1500 1270.sin.NNθ.(b)θ=°57 9.θy0.127 Nxθ0.150 NT yFIG. P3.66(a)The y-components for the forces must add to zero:+−°=Ty0 15057 90.cos.Naf, Ty=0 079 8.N .(c)The angle between the yaxis and the horizontal is 90 057 932 1...°−°=°.P3.67The displacement of point Pis invariant under rotation ofthe coordinates. Therefore, rr=′and rr22=′b gor,xyxy2222+=′+′b gb g. Also, from the figure, βθα=−∴′′FHGIKJ=FHGIKJ−′′=−+−−tantantantan111yxyxyxyxyxαααe je jxyyPOtβαθβα′rx′FIG. P3.67Which we simplify by multiplying top and bottom by xcosα. Then,′
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