Question

what is the forces that effects the roller coaster ? can you show me a graph showing these forces?

Answer 1

Let us assume that there are negligible amounts of air resistance acting upon the riders in the roller coaster.

Thus, the only forces exerted upon the riders are the force of gravity and the normal force (the force of the seat pushing up on the rider). The force of gravity is at all times directed downwards and the normal force is at all times directed perpendicular to the seat of the car. Since the orientation of the car on the track is continuously changing, the normal force is continuously changing its direction. The magnitude and direction of these two forces during the motion through the loop are depicted in the animation below.

The diagram below depicts the free-body diagrams for a rider at four locations along the loop. The diagram also shows that the vector sum of the two forces (i.e., the net force) points mostly towards the center of the loop for each of the locations.

Feelings of weightlessness and heaviness are associated with the normal force; they have little to do with the force of gravity. A person who feels weightless has not lost weight. The force of gravity acting upon the person is the same magnitude as it always is. Observe that in the animation above the force of gravity is everywhere the same. The normal force however has a small magnitude at the top of the loop (where the rider often feels weightless) and a large magnitude at the bottom of the loop (where the rider often feels heavy). The normal force is large at the bottom of the loop because in order for the net force to be directed inward, the normal force must be greater than the outward gravity force. At the top of the loop, the gravity force is directed inward and thus, there is no need for a large normal force in order to sustain the circular motion. The fact that a rider experiences a large force exerted by the seat upon her body when at the bottom of the loop is the explanation of why she feels heavy. In actuality, she is not heavier; she is only experiencing the large magnitude of force which is normally exerted by seats upon heavy people while at rest.