Hard/Tricky Problem on Energy Conservation

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SUMMARY

The problem involves determining the maximum radius R for a car moving at an initial speed of 4.0 m/s to maintain contact with a circular track. The relevant equations include the potential energy (PE = mgh), kinetic energy (KE = (1/2)mv²), and centripetal force (Fc = mv²/R). The initial assumption that the car has zero velocity at the top of the circle is incorrect, as the car must maintain contact throughout its motion. This problem is sourced from "Physics 6th Edition" by Cutnell & Johnson.

PREREQUISITES
  • Understanding of potential energy (PE) and kinetic energy (KE) concepts
  • Familiarity with centripetal force (Fc) calculations
  • Basic knowledge of circular motion dynamics
  • Ability to interpret physics problems from textbooks
NEXT STEPS
  • Study the relationship between centripetal force and gravitational force in circular motion
  • Learn how to derive conditions for maintaining contact in circular motion
  • Explore the implications of varying initial speeds on circular motion dynamics
  • Review examples of similar problems in "Physics 6th Edition" by Cutnell & Johnson
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators looking for problem-solving strategies in energy conservation scenarios.

ShamTheCandle
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Homework Statement


If the car is given an initial speed of 4.0 m/s, what is the largest value that the radius R can have if the car is to remain in contact with the circular tract at all times?
See the attached file (named: car.pdf) for the drawing.

Homework Equations


PE=mgh ----> Formula for Potential Energy
KE=(1/2)mv² ----> Formula for Kinetic Energy
Fc=mv²/R ----> Formula for Centripetal Force

The Attempt at a Solution


My initial attempt was to assume that the car has zero velocity at the top of the circle. However this is not true, since the car should "remain in contact with the circular tract at all times". This is an even problem from my textbook, so no answer is given in the back. By the way, I am referring to "Physics 6th Edition" by Cutnell & Johnson.

Thank you for helping!
 
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