Kinetic and poetenial energy of a roller coaster loop

AI Thread Summary
The discussion revolves around calculating the normal force (Fn) of a mass m traveling down an incline and through a loop, with the problem requiring an understanding of kinetic and potential energy. The key equations involved are potential energy (U = mgh) and kinetic energy (k = 1/2 mv^2). The participant expresses confusion about whether to create separate equations for different angles or a single equation that encompasses all angles from 0 to 180 degrees. They recognize that the velocity at the loop's apex is v = sqrt(2gh) and seek clarification on the forces acting on the body at various points in the loop. The conversation emphasizes the importance of understanding energy transformations and force directions throughout the motion.
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Homework Statement


O.k, i'll do my best to explain the problem as I but a picture would probabley be helpful. Basically there's an object of mass m travlleing down an incline. Near the end of the incline it does a loop. The question asks to calculate the normal force(Fn) as a function of ө for 0 ≤ ө ≤ 180 (assume cart is from height h) hint: your answer will depend on m, g, h, r and ө. Check that equation has proper behavior ө= 0 degrees, 90 degrees and 180 degrees.


Homework Equations




U= mgh

k=1/2mv^2


The Attempt at a Solution



i understand what's going on it's just putting it into an equation that I find difficult. I am assuming that ө equals zero at the appex before the ascent into the loop. Also, kinetic energy increase as ө increase i think. I'm just no sure if I should do three separate equations or one if just one then how can it represent all three angles? Any help will be greatly appreciated!
 
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After looking at this problem some more I see that the equation kind of looks like the sine function am I on to something?
 
Please could someone help me?
 
When the body reaches the appex of the loop ita velocity will be v = sqrt(2gh). What are the forces acting on the body at this point and what are there direction? As the body moves along the loop, what are the directions of these forces?
 

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