It is possible to estimate the effectiveness of sweeping action in curling?
I mean how can the sweepers carry forward the stone it they do sweeping action all over the rink?
Yes it is possible to estimate the effectiveness of sweeping on a curling rock. There have been numerous studies to determine the answer to this question. I have personally participated in several of these studies.
These studies often involve a rock throwing machine which is able to throw the rock on a consistent trajectory, with a consistent speed and rotation (Sometimes it can just be a human throwing them as well but those results are not as robust as there is more variance in a human thrower than a robot.) After the rock is released, you have a group of sweepers that either sweep the rock or leave it alone. There can be variations on this where sweepers try different techniques or try different broom heads.
In short, 3 - 9ft is the distance that can be added to a rock when swept. However whether you get 3ft or 9ft depends on many factors such as: ice temperature, air temperature, humidity, frost, type of pebble, type of broom, strength of sweeper, running surface of the rock.
In general, the keener the ice, the more distance a rock can be dragged and earlier in the game is when sweeping is most effective.
The entire sport of curling is an example of Newton's first law of motion - "An object a rest tends to remain at rest, and an object in motion tends to continue in moving in a straight line at constant speed unless an outside force acts upon it."
The sweeping action is to smooth out the ice, and prevent the friction from the bumps in the ice slowing down the stone. Hence sweeping at one side will only smooth out the ice on that side, causing the stone to curve.
I'm not sure you could exactly quantify the effectiveness of the sweeping action - it would depend on so many variables, such as initial bumpiness of the ice, strength of the sweeper, abrasive quality of the broomhead, force exerted on the broom etc.