The radius of the loop decreases as the carts enter and exit the loop.
We know that the centripetal acceleration is inversely proportional to the radius of the loop.
Variation in your apparent weight is desirable when you ride a roller coaster; it makes the ride fun. However, too much variation over a short period of time can be painful. For this reason, the loops of real roller coasters are not simply circles like (Figure 1) . A typical loop is shown in(Figure 2) . The radius of the circle that matches the track at the top of the loop is much smaller than that of a matching circle at other places on the track.
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