Question

2-4. Determine the magnitude of the resultant force acting on the bracket and its direction measured counterclockwise from the positive u axis.

Answer 1

solution

Determine the magnitude of the resultant force acting on the bracket and its direction measured counterclockwise from the positive u axis.

The parallelogram law of addition the triangular rule are shown in Figs, a and b, respectively.

Applying the law of cosines to fig. b

$F_R=\sqrt{200^2+150^2-2(200)(150)cos75°}$

      $=216.721b=2171b$               ans.

Applying the law of cosines to fig. b and using this result yields.

$\frac{sin \alpha}{200}=\frac{sin75°}{216.72}=>\alpha=63.05°$

So, the direction angle $\phi$ of $F_R$, measured counterclockwise from the positive u axis, is $\phi$=3.05°

 

 

Answer.

Thus, the direction angle $\phi$ of $F_R$, measured counterclockwise from the positive u axis, is $\phi$=3.05°