When we think of coasters we usually think about them converting potential energy into kinetic energy, but modern coasters do not move in simple straight lines. Turns and loops bring up new questions of physics because they alter the forward momemtum that results from dropping the coaster down the first hill.
Remembering Newton's law--an object in motion will continue in motion along a straight line, you realize that passengers going have momentum pushing them straight forward. On a level turn, passengers are moving forward as the train turns...and as a result, they move to the outer side of the car. The side of the car then exerts the force that takes them through the turn. Coaster designers realized that they could make a ride more comfortable (passengers not squishing each other) and safer by banking the curves. By banking the curve, most of the force that pushes the passengers through the curve comes from the seat rather than the side of the train.
On a looping coaster, the general rules of centripetal force are in operation because the train is making a turn at every point during the loop--- remember Newton's first law that an object in motion will stay in motion unless another unbalanced force acts on it. The force that makes the train turn through the loop is centripetal force. The formula for the amount of centripetal force needed to move an object in a circular route is:
To complete a vertical loop, a train must enter the loop with sufficient kinetic energy to reach the top of the loop and still be moving. It then has converted kinetic energy into potential energy and starts down the other side of the loop, and accelerates out of the loop. When the train starts into the loop, the track supplies the force to make the train turn (the seat force). As the train comes down the hill to enter the loop, it's gravitational force and momentum are pushing it toward the ground while the seat force is pushing upward. How much seat force it takes to change the direction of the train is determined by the train's weight and speed (mass X velocity). The more seat force it takes to start the loop, the more "G FORCES" the passengers will feel.
As the train starts the loop, gravity and momentum are pulling the train out of the loop, so the structure of the track provides the "seat force" that moves the train through the loop--the centripetal force. On it's upward climb, the train reaches a point where gravity is no longer pulling it out of the loop and thereafter it is acting as part of the centripetal force pulling the train toward the center of the circle. It is from this point until the top of the loop that it is important that the train has enough momentum to counteract the forces pulling it toward the center of the loop. That is a unique aspect of centripetal force on a vertical axis--there must be enough outward momentum to counteract the increase in centripetal force that occurs in the upper portion of the loop.
Once the train reaches the top, potential energy is again converted to kinetic energy and the train accelerates as it travels down the other side of the loop.
Because the passenger is being pushed into his/her seat as they go through the loops, the brain is fooled by the inversion. It interprets the pressure in the seat as indication he/she is in an upright position. The visual image still gives the passenger the awareness of the loop without the fear of falling. In fact, because the you are being pushed into the seat, you could ride through the loops without the shoulder straps--the straps are added for psychological security.
Next time you are on a looping coaster, use the accelerometer to measure your "g's" at the bottom of the loop and again at the top. Are the laws of physics being obeyed?
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