1) A roller coaster makes a vertical circle (loop-the-loop)with a radius of curv

Question

1) A roller coaster makes a vertical circle (loop-the-loop)with a radius of curvature of 12.7 m. At what minimum speed (inm/s) must a roller coaster car be traveling when upside down at thetop of a circle so that the passengers are not to fall out if theyare not strapped in? ( Ans: 1.12x10^1)
2) A8.1-kg puck, attached to the end of a horizontal string, is rotatedin a circle of radius 2.2 m on a frictionless horizontal surface.If the string will break when the tension in it exceeds 91.2 N,what is the maximum speed the puck can have? ( Ans:4.98x10^0 )
1) A roller coaster makes a vertical circle (loop-the-loop)with a radius of curvature of 12.7 m. At what minimum speed (inm/s) must a roller coaster car be traveling when upside down at thetop of a circle so that the passengers are not to fall out if theyare not strapped in? ( Ans: 1.12x10^1)
2) A8.1-kg puck, attached to the end of a horizontal string, is rotatedin a circle of radius 2.2 m on a frictionless horizontal surface.If the string will break when the tension in it exceeds 91.2 N,what is the maximum speed the puck can have? ( Ans:4.98x10^0 )

Explanation / Answer

Radius r= 12.7 m If the centrifugal fiorce is equal to weight then they willnot fallout i.e., mv ^ 2 / r = mg from this required speed v = [ rg ]                                         = 11.156 m / s (b). masss m = 8.1 kg radius R = 2.2 m Maximum tension T = 91.2 N Maximum speed V = ? we know T = mV ^ 2 / R from this V = [ TR / m ]                   = 4.977 m / s

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