Acceleration of a Roller Coaster

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Serway, Raymond A., Faughn, Jerry S., Moes, Clement J. College Physics Sixth Edition. Pacific Grove, California: Thomson Learning. 2003. "Assume the speed of the roller coaster is 12.0 m/s at the top of the loop, which has radius 8.00 m. Find the force exerted by the seat on a 70.0 kg passenger. Then assume the speed remains the same at the bottom of the path and find the force exerted by the seat on the passenger at this point." top of loop 0.8 g
bottom of loop 2.8 g
Acceleration Stress. Encyclopedia Britannica. 1999. "AT THIS POINT IN THE RIDE … the coaster approaches the vertical loop, entering at a high rate of speed. Entry may create a heavy force on the riders as high as 5 g, but only for a few seconds--any longer and riders may blackout from acceleration stress. Modern vertical loops are tear-shaped, clothoid loops that have a tighter curve at the top, where the velocity is smaller, than at the exit and entry points at the bottom. The larger radius at the bottom of the loop reduces centripetal acceleration, thereby lowering the overall g-forces, which naturally increase by 1 g owing to gravitation. Often the designer will adjust the radius at the top of the loop to create a centripetal force of 2 g, allowing the riders, after subtracting the value of gravitation (1 g), to experience normal weight levels while upside down. The queasiness associated with looping rides is owing to some internal organs floating upward, counter to their natural hanging position." top of loop 2.0 g
bottom of loop 5.0 g
Taylor, Richard L. CBL Measurements at Six Flags Over Texas.The Hockaday School, Dallas, Texas. June 2006. min. 0.9 g
max. 5.0 g
Homer. Revolution. Six Flags Magic Mountain. Valencia, California. June 2006. "Acceleration: Positive G's 4.9 G's" max. 4.9 g
Batman and Robin: The Chiller. Wikipedia. 28 May 2006. "Max G force 5" max. 5.0 g

As a rider starts the descent down the first drop of a roller coaster, she begins a one-minute adventure filled with various sensations of weightlessness, heaviness, and jerkiness. G-forces explain the various sensations experienced on a roller coaster loop (1 g = 9.8 m/s2).

A person who feels weightless has not lost weight. The force of gravity acting upon the person is the same magnitude as it always. The normal force however has a small magnitude at the top of the loop (where the rider often feels weightless) and a large magnitude at the bottom of the loop (where the rider often feels heavy). Most roller coasters have acceleration between 2 g and 5 g. At the top of the loop, the gravity force is directed inward and thus, there is no need for a large normal force in order to sustain the circular motion. The formula for centripetal acceleration ac = v2/r was used to determine the top and bottom acceleration of a ride. After entering the values, the top and bottom g-forces were determined 0.8 g and 2.8 g.

A rider feels heavy at the bottom of the loop because of the large force (five times her weight) exerted by the seat upon her body. Batman and Robin: The Chiller, Shockwave and Magic Mountain rides at Six Flags respectively have a maximum acceleration of 5.0 g, 5.0 g, and 4.9 g. In actuality, she is not heavier; she is only experiencing the large magnitude of force that is normally exerted by seats upon people while at rest.

Saintedym Wills -- 2006

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