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In the previous example, what is the minimum speed necessary to keep the roller coaster on the track at all times? |
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Answer» Solution :The position where the roller coaster is most in danger of leaving the track is at the top. `F_(N)+F_(w)=(mv^(2))/(r)` The SLOWER the OBJECT moves, the smaller `F_(N)` gets (`F_(W)` is a constant). Therefore, the minimum speed occurs when `F_(N)=0`. (for a MOMENT, the ROLLERCOASTER is touching the track but not pressed against it: it's almost losing contact.) `F_(w)=(mv^(2))/(r)` `mg=(mv^(2))/(r)` `v=sqrt(gr)` |
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