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Motion Along Curved Paths definitions

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  • Curved Path Problem
    A scenario where an object moves along a path with a constantly changing slope angle, complicating force and kinematic analysis.
  • Energy Conservation
    A principle stating that the total energy in a closed system remains constant, used to solve problems with non-constant acceleration.
  • Kinetic Energy
    The energy an object possesses due to its motion, calculated as 1/2 times mass times velocity squared.
  • Potential Energy
    The energy stored in an object due to its position in a gravitational field, calculated as mass times gravity times height.
  • Non-conservative Forces
    Forces that cause energy dissipation from a system, such as friction, not present in the given problem.
  • Gravitational Potential Energy
    Energy an object possesses due to its height above a reference point, contributing to total mechanical energy.
  • Minimum Speed
    The lowest velocity required for an object to reach a certain point without falling short.
  • Acceleration due to Gravity
    The constant rate at which objects accelerate towards Earth, approximately 9.8 m/s².
  • Hill Height
    The vertical distance from the base to the top of a hill, given as 20 meters in the problem.
  • Initial Conditions
    The starting parameters of a problem, including initial kinetic energy and zero potential energy at the base.
  • Final Conditions
    The parameters at the end of a problem, including zero kinetic energy and maximum potential energy at the hill's peak.
  • Velocity
    The speed of an object in a specific direction, crucial for determining kinetic energy.
  • Mass Cancellation
    A simplification in energy equations where mass is eliminated from both sides, focusing on velocity and height.
  • Square Root Calculation
    A mathematical operation used to solve for velocity in energy equations, involving the square root of 2g times height.
  • Smooth Hill
    A surface with no friction, ensuring no work is done by non-conservative forces in the problem.