Hi, can you please help me solve the following problem? It\'s notfrom a textbook

Question

Hi, can you please help me solve the following problem? It's notfrom a textbook, but we use the Giancoli Textbook as a resource.Thank you! Please provide step by step process of how youapproached the problem.

A roller coaster car begins a drop from a height of 30m from theground with initial speed of 10m/s. The bottom of the first troughis at a height of 2m from the ground, and its radius of curvatureat the lowest point is 10m. Then the car climbs to a peak at aheight of 15m from the ground, where the radius of curvature at thehighest point is 8m. Ignore friction and air resistance.

a) How many gs do the riders feel at the bottom of thetrough?

b) Would an unstrapped rider be flying off her seat at the top ofthe 15m high peak?

Explanation / Answer

From law of conservation of energy , Loss in potential energy = Gain in kinetic energy Here for the first trough , Loss in potential energy = mg(H-h ) = mg(30-2 )= 28 mg Initial kinetic energy = mv2/2 = 50m Gain in kinetic energy = Final - initial kinetic energy So Final Kinetic energy - 50m = 28mg So Final Kinetic energy = 324.4m Let velocity at that time be V Then Kinetic energy =mV2/2 Putting the value mV2/2 = 324.4m V=25.47 m/s Also centrifugal acceleration felt = v2/r Putting the value for first trough Centrifugal acceleration = 25.472/10 = 64.9m/s2 =6.62 g Again for the 15 m peak , Comparing to initial stage , Loss in potential energy = Gain in kinetic energy Loss in potential energy = mg(30-15 )= 15 mg Initial kinetic energy = mv2/2 = 50m Gain in kinetic energy = Final - initial kinetic energy So Final Kinetic energy - 50m = 15mg So Final Kinetic energy = 197m Let velocity at that time be V Then Kinetic energy =mV2/2 Putting the value mV2/2 = 197m V=19.85 m/s Also centrifugal acceleration felt = v2/r Putting the value for 15 m peak Centrifugal acceleration = 19.852/8=49.25m/s2 As this acceleration is more than acceleration due to gravity , So unstrapped rider will be flying off his seat at the top ofthe 15m high peak

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