Answer to Question #78051 in Mechanics | Relativity for Charvi

Question

When we apply force on the doors of our house for some time they get moved but stop at some point then what is the reason behind that when there is no friction between gate and floor or something else
And one more question that why we have to latch the door to keep it stationary at its position why doesnt force bexcomes enough to close to its fullest

Answer 1

A net force on an object likes to act through the centre of mass of that object; in this case, the middle of the door. Apply a force to the centre of mass and it will accelerate uniformly because there is an even amount of matter on all opposing sides that can resist the motion with an even amount of inertia. If a force is applied off the centre of mass, it will cause rotations because there is now one side that contributes more inertia than its opposing side. The opposing side, therefore, accelerates faster and the result is rotation. However, you still only have one applied force and the total acceleration applied to the centre of mass must obey Newton's Second Law. So if one side is accelerating faster than the centre of mass, the other side must accelerate slower to compensate. That is for a free object (not fixed by a hinge or anything).
For the door, it's very similar except that the hinge end cannot move. If you apply force at the hinge, it won't rotate because all of that force will be opposed by the wall to prevent the hinge from moving, so the door won't move. As the applied force moves away from the hinge, the process I described in the above paragraph kicks in. The more of the door is on the same side of the force as the hinge, the more inertia that side produces and the slower it accelerates. Again, because the hinge can't move, it provides an opposing force. But if that side accelerates slower, then the opposing force decreases and your net force increases (that means the door becomes easier to accelerate). As you move to the other end of the door, the hinge can actually gain the desire to accelerate backwards (like I described above), so the opposing force would push back in the same direction as the applied force. This makes the free end accelerate faster to compensate, thus rotation occurs.