The amount that gravity pushes the rider into the seat is the gravitational constant multiplied by the cosine of the angle the rider is traveling. To account for problem 2, we must also vary the radius, but this time as a function of the angle of travel instead of the height. So to account for problem 1 and maintain constant acceleration, we must take our circular loop and bend it so that it has a smaller radius as the height increases. However, if an entire loop were a circle with constant radius, there would be two big problems:ġ. The roller coaster slows down as it climbs the loop, so centripetal acceleration would drop near the top.Ģ. Gravitational acceleration and centripetal acceleration are additive at the bottom of the loop, where they both push the rider into the bottom of the seat, but opposite at the top of the loop, where centripetal acceleration pushes the rider into the seat, but gravity tries to pull him out. Where A is the acceleration, V is the velocity, and r is the radius. The centripetal acceleration around a circle is expressed as: So, like gravity, the centripetal force can be expressed as acceleration and applied to any sized person. The force is a function of speed and radius, but, just like gravity, is proportional to the rider’s body mass. Traveling around a circle creates a centripetal force that the rider experiences as a G-force. To create a constant G-force loop, you can start with the basic shape of a circle. We asked what shape to start with, and how to modify it to make the loop. Last month's challenge was define the shape of a roller coaster loop that would create a constant G-force experience.
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