Variation in your apparent weight is desirable when you ride a roller coaster; i

Question

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 6.21a. A typical loop is shown
on the right. 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. Explain why this shape gives a more comfortable ride than a
circular loop.

Explanation / Answer

The tighter the curve, the greater the centripetal force. The greater the centripetal force is, you feel a stronger force pushing you into the floor of the roller coaster. Gravity always pulls down, the force you feel pushing you into the seat always pulls towards the outside of the loop. When gravity and the turning force are pointing in the same direction, they make the curve loose so you don't feel as much weight gain. When gravity and the turning force are in opposite directions (at the top) they can make the loop tighter because the gravity pulling you down will counter-act the turning force pulling you up. If it was a perfect circle, that turned hard enough to create an apparent force equal to that of gravity, at the top they would cancel out perfectly, and you would feel weightless. At the bottom, however, they would add together and you would feel like you weigh twice as much as you normally do.

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