At the bottom of a roller coaster loop, the normal force is greater than the weight (mg) of the object undergoing circular motion. This is necessary to provide the centripetal force required to keep the object moving in a circular path.
In circular motion, there must be a net inward force acting on the object, directed toward the center of the circle. This force is called the centripetal force. In the case of a roller coaster loop, the centripetal force is provided by the combination of the normal force and the force of gravity.
The normal force is the force exerted by a surface perpendicular to the object in contact with it. In the case of a roller coaster, the normal force acts in an upward direction from the track to counteract the force of gravity pulling the object downward.
At the bottom of the loop, the object experiences an apparent weight increase due to the combination of the acceleration from the circular motion and the force of gravity. This apparent weight increase is greater than the actual weight of the object (mg) and is given by:
Apparent weight = Normal force - Weight
To maintain circular motion, the apparent weight must provide the necessary centripetal force. Therefore, the normal force must be greater than the weight to provide the additional upward force required for the object to follow the curved path without falling off the track.
In summary, the normal force is greater than the weight at the bottom of a roller coaster loop to provide the additional force (centripetal force) necessary for the object to maintain circular motion and prevent it from leaving the track.