Three forces with magnitudes 16 N, 12 N and 21 N are shown in the diagram below. Determine the magnitude of their resultant force and angle with the x-axis
Fx= 12cos32°-16cos26° = -4.20N (right is taken +ve and left is taken -ve) Fy=12sin32°+16sin26°-21 = -7.63N (up is taken +ve and down is taken -ve) R2= 4.202+7.632 ⇒R2 = 75.86 ⇒ R=√75.86 ∴R = 8.71 N tan θ=oppadj
⇒tan θ=7.634.20 ⇒tan θ =1.8095 ⇒ θ = tan−1 (1.8095) θ = 61°
∴The angle of the resultant force with the x-axis is 61°
