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# Speed of loop-de-loop roller coaster at the top of a circle

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At what minimum speed must a roller coaster be traveling when upside down at the top of a circle if the passengers are not to fall out? Assume a radius of curvature of 9.27 m.

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-For problems of this type, my strategy would be to always begin with a free-body diagram. Don't be too intimidated by the apparent lack of information: often many of the parameters will drop right out of the equations involved.
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-In this case, consider the forces acting on the people in the roller coaster. At all times, they will have 2 forces acting on them:
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-1) Force of gravity (mg)
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-2) Normal force, i.e. force of contact on their bodies from the seat they are sitting on.
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-Note that force of gravity will stay constant, and always point down, while the normal (contact) force will vary (you have probably felt the difference in how firmly you are in contact with the seat during such roller coaster rides!). Also, the ...

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