The Conservation of Mechanical Energy

AI Thread Summary
The discussion revolves around a physics problem involving a skier descending from a hill and losing contact at the crest of a second hill with a radius of 45 m. Key concepts include the conservation of mechanical energy, where potential energy at the first hill equals the sum of potential and kinetic energy at the second hill. Participants emphasize the need to consider centripetal acceleration at the top of the second hill, where the skier's weight minus the normal force equals the required centripetal force. The critical point is to derive an expression for the height of the first hill in terms of the radius of the second hill's curvature. Understanding these relationships is essential for solving the problem accurately.
zizikaboo
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help I'm really stuck on this question!
A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill. The crest of the second hill is circular, with a radius of r = 45 m. Neglect friction and air resistance. What must be the height h of the first hill so that the skier just loses contact with the snow at the crest of the second hill?

um. i know it has to do with 1/2m(vf)^2+mghf=1/2mv0^2+mgh0 but i just don't really understand what the question meant by 2nd hill and its radius!
 
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Think of the centripetal acceleration as he is at the top of the second hill?
What does the acceleration need to be if he barely going to lift off?
 
By conservation of energy :

PE at start (crest of first hill) = (PE + KE) at end (crest of second hill).

Also, while moving in a circular trajectory on the second hill,

Weight of skier - Normal reaction force = Centripetal force.

What happens to the reaction force when the guy just loses contact ?

What's the expression for the centripetal force in terms of mass, velocity and radius ? How is it related to the expression for kinetic energy ?

Now plug in the expressions for each of those and solve for the height in terms of the radius of curvature of the crest of the second hill.
 
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