Solving the Physics of a Skier Leaving a Hill

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SUMMARY

The discussion focuses on the physics problem of a skier leaving a hemispherical hill, specifically demonstrating that the skier becomes airborne at a height of h = R/3 below the top of the hill, where R is the radius of the hill. The solution involves applying the principles of conservation of energy and analyzing forces, particularly when the normal force acting on the skier reaches zero. Key equations include the conservation of energy and the centripetal force equation, m(v²/r).

PREREQUISITES
  • Understanding of conservation of energy principles in physics
  • Knowledge of centripetal force and its equation, m(v²/r)
  • Familiarity with the concept of normal force in mechanics
  • Basic skills in solving physics problems involving forces and motion
NEXT STEPS
  • Study the application of conservation of energy in mechanical systems
  • Learn about the conditions under which normal force becomes zero
  • Explore centripetal motion and its implications in real-world scenarios
  • Investigate projectile motion to understand the skier's trajectory after leaving the hill
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of motion on curved surfaces, particularly in relation to forces and energy conservation.

austindubose
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Homework Statement


A skier starts from rest at the top of a large hemispherical hill. Neglect friction and show that the skier will leave the hill becoming airborne at a distance of h=R/3 below the top of the hill. R is the radius of the hemispherical hill.


Homework Equations


Conservation of energy, balancing of forces, centripetal force = m(v2/r)


The Attempt at a Solution


I know this has to do with when the normal force becomes zero (or at least that's what I think). But I have no idea how to start this; can anyone point me in the right direction?
 
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