Question

You are riding on a roller coaster and sitting on a bathroom scale. Where on the ride will you weight the most? Explain using a force diagram.

Answer 1

A roller coaster is a machine that uses gravity and inertia. The g-forces and centripetal acceleration give the body certain sensations in a winding track i.e. the feelings of weightlessness and heaviness. The motion along a coaster loop is not precisely a circular motion at constant speed since the loop is neither circular nor the speed constant. The riders experience the sensation of a centrifugal force (a pseudo force) pushing them toward the outer edge of the track though like g-force it’s not really a proper force. This sensation is actually the result of the rider's inertia. In the loop-the-loop upside down design, it’s inertia that keeps you in your seat. The loop however must be elliptical, rather than a perfect circle, otherwise the centrifugal force would be too strong for safety and comfort. In modern roller coaster, the loop-the-loops are shaped more like teardrops shape. The key factor is the fact that the loop has a smaller radius on top.

The ride will weight most at the bottom of the roller coaster loop. Here, I am giving explanation for it.

The normal reaction force (N) has a small magnitude at the top of the loop (rider feels weightlessness) and a large magnitude at the bottom of the loop (rider feels heaviness). The value of N is large at the bottom of the loop because the net force to be directed inward, N 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 N in order to sustain the circular motion.

In the elliptical loop/circular loop, the normal reaction force and the weight act in the same direction at the top of the loop. These force are balanced by the centrifugal force. That is why the normal reaction will be less than the weight. On the other hand, at the bottom of the loop the weight and normal reaction act in opposite direction. Now, the normal reaction is balanced by the weight plus the centrifugal force. Hence the normal reaction will be greater than the weight.