Centripetal Motion on a Semi-Rollercoaster

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SUMMARY

The discussion focuses on analyzing centripetal motion on a roller coaster with a radius of 36.9 meters and a speed of 160 km/h. The user seeks to calculate centripetal acceleration using the formula a_centripetal = v^2/r while ascending. Additionally, they require guidance on determining acceleration and velocity during the free fall from a height of 115 meters, referencing an exponential decay function f(x)=exp(-x) to describe the curve's shape.

PREREQUISITES
  • Understanding of centripetal acceleration and its formula a_centripetal = v^2/r
  • Knowledge of kinematic equations for motion under gravity
  • Familiarity with exponential functions and their graphical representation
  • Basic principles of physics related to roller coaster dynamics
NEXT STEPS
  • Study the application of kinematic equations in free fall scenarios
  • Learn about the effects of gravitational acceleration on roller coasters
  • Explore advanced topics in centripetal force and motion analysis
  • Investigate the mathematical modeling of roller coaster trajectories
USEFUL FOR

Physics students, mechanical engineers, and amusement park designers interested in the dynamics of roller coasters and motion analysis.

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http://cache.rcdb.com/pictures/picmax/p5740.jpg
I am doing an analysis on a roller coaster that is represented on the diagram attached.

However, I am having trouble analysing the curve. The radius is 36.9m and it is 160km/hr going up and then it free falls back down from 115m for about three seconds.
When I am going up do I just use a_centripetal = v^2/r to find the acceleration?
When I am going down, I have to find the acceleration as well as the velocity, but how do I know where to start?
 
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u know the figure look like a function f(x)=exp(-x).
the above function mean that "x" is linear and than it decay exponentially as u can see in ur figure.
 

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