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
A.
7.63N,61°
B.
8.71N,61°
C.
7.63N,29°
D.
8.71N,29°
Correct answer is B
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)
\(R^2\)= 4.202+7.632
⇒\(R^2\) = 75.86
⇒ R=√75.86
∴R = 8.71 N
tan θ=\(\frac{opp}{adj}\)
⇒tan θ=\(\frac{7.63}{4.20}\)
⇒tan θ =1.8095
⇒ θ = \(tan^-1\) (1.8095)
θ = 61°
∴The angle of the resultant force with the x-axis is 61°