Question

A block of mass $m=10kg$ is pulled by a force $F=100N$ at an angle $\theta ={30}^o$ with the horizontal along a smooth horizontal surface. What is the acceleration of the block? $(g=10m/s^2)$

Answer 1

The $F.B.D$ of the block shows the force components Along $X-$axis, let the acceleration of the block be ${}^{\prime }{a}^{\prime }$
$\Rightarrow F\cos \theta =ma$ ...$\left(1\right)$
$\Rightarrow a=\frac{F\cos \theta }{m}$ ...$\left(2\right)$
$=\frac{100\cos {30}^o}{10}=\frac{100\sqrt{3}}{2\times 10}=5\sqrt{3}m/s^2$
$\therefore$ the acceleration of the block is $5\sqrt{3}m/s^2$ directed towards right. Since $F\sin \theta <mg$ & the surface is rigid, the block remains in equilibrium along $Y-$ axis.