A $ 2.0 kg $ block is being pulled across a frictionless table by a rope with negligible mass at an angle $ \theta=60° $ (from positive direction of $ x $ axis, we have taken horizontal surface of table as $ x $ axis) The tension in the rope is $ 12N $ and causes the box to slide across the table to the right with an acceleration of $ 3.0 m/s² $ But the direction of net force is along the rope. The direction of acceleration isn't. Why is that? There is a net vertical force and that force is vertical component of tension force. The gravitational force is balanced by the normal force (the magnitude of normal force and gravitational force are always same). Why is the acceleration only along horizontal component of tension force. It should be along the the net tension force (along the rope)
The acceleration is always in the direction of the net force (Newton's Second Law). In your example, if you simply resolve all the forces in the vertical and horizontal directions, you can see why.
The basic assumption here is that the gravitational force is balanced by both the normal reaction from the table and the tension component in the vertical direction. As there is now a horizontal force along the table, it accelerates as such.