Two Brainmelting Problems Save Me

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The discussion revolves around two challenging physics problems related to work-energy concepts. The first problem involves determining the maximum radius of a loop for a car traveling at an initial speed of 4.0 m/s, ensuring it remains in contact with the track. The second problem requires calculating the height of a hill from which a skier must start to just lose contact with the crest of a second hill with a radius of 36m. Participants emphasize the importance of equating centripetal force to gravitational force at the loop's top and analyzing energy conservation between potential and kinetic energy. Clear explanations and guidance are provided to help understand the underlying physics principles.
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These two are toughies for a first year rookie like me. I survived kinematics, and I thought I survived circular motion. But the work-energy chapter just threw 2 curveballs in my face. Any help would be more than appreciated:

1) The drawing shows a version of the loop-the-loop trip for a small car (the picture sucks. its basically a real circle, car goes straight ahead then up and around the loop and out the other side) If the car is given an inital speed of 4.0 m/s. What is the largest value that the radius can have if the car is to remain in contact with the circular track at all times? :cry:

2) A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill, as the drawing illustrates (the skier starts from an unkown height above a horizontal, the slope goes downward under the horizontal, and comes back up on the second "circular" crest). The crest of the second hill is circular, with a radius of 36m. Neglect friction and air resistance. What must be the height of the first hill so that the skier just loses contact with the crest of the second hill?

The first one I've been struggling with for hours. The second one, I'm not sure i understand the question, so if you explained it to me, I could probably figure it out myself
 
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1. Adjust the centripetal force such that the force required to keep it moving in a circle is equal to the force of gravity at the top of the ramp (keep in mind the change in potential energy with the movement up the loop)

2. Same idea. Start off with expressing the potential energy of the object at the top (mgh). At the bottom of the hill, all of that potential energy is converted to kinetic energy and then partially converted back to potential energy partially. The remainder of the kinetic energy is just enough to cause gravity to simulate circular motion about that circular hill. I hope I made this clear enough.
 
Thats exactly what i needed to hear. THanks a lot vsage
 
Anytime :) Good luck with those.
 

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