The magnitude of F is 12.47 N.
Given data:
The mass of block is m=3.37548 kg.
The accleration of block is a=3.2 m/s².
The magnitude of applied force F can be calculated by applying the Newton's second law,
[tex]\begin{gathered} \sum ^{}_{}F_{net}=ma \\ F\cos \theta=ma \\ F\cos 30\degree=(3.37548kg)(\frac{3.2m}{s^2})\times\frac{1\text{ N}}{\frac{1kgm}{s^2}} \\ F=\frac{10.801536\text{ N}}{\cos 30\degree} \\ F=12.47\text{ N} \end{gathered}[/tex]
Thus, the magnitude of F is 12.47 N.
