Kinetic and poetenial energy of a roller coaster loop

[Cate]

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!

 

[Cate]

After looking at this problem some more I see that the equation kind of looks like the sine function am I on to something?

 

[Cate]

Please could someone help me?

 

[rl.bhat]

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?