Question

According to Newton's second law of motion, resultant force on a particle is in the direction of acceleration of the particle.

Two forces $F_{1}$ and $F_{2}$ are acting on a particle as shown in the figure. The acceleration of the particle is along $X$-axis. The value of $F_{1}$ (in newton) is ____

Answer 1

Since, acceleration of particle is along $X$-axis.
So, net forces will be along $X$-axis.
Hence, $\sum F_{Y}=0$
$\therefore F_{2} \sin 37^{\circ}-F_{1} \sin 30^{\circ}=0$
or $ \frac{3}{5} F_{2}=\frac{F_{1}}{2} $
$\therefore F_{1}=\frac{6}{5} \times 5=6\, N$