Conservation of Enery (roller coaster)

[Carpe Mori]

ok i this question has been asked but whoever asked it did not show work therefore did not have it answered so here we go my attempt!

Homework Statement

Show that on a roller coaster with a circular vertical loop the difference in your apparent weight at the top of the loop and the bottom of the loop is 6 g's that is 6 times your weight. ignore friction.

h = height of start of roller coaster
R = loop's radius

Homework Equations

PE = KE
a = v^2/R

The Attempt at a Solution

at the top of loop: mgh = mg2R + .5mv^2
solved for velocity v^2 = 2g(h-2R)
centripetal acceleration is a = v^2/R ---> a = 2g(h-2R)/R

also i knew from another problem that minimum h had to be 2.5R to be able to go through the whole loop and stay on track so...

a = g? haha yeah i am lost i have no idea what to do. I am trying to teach this course to myself and i am really struggling without a teacher. Please help?

 

[Dick]

Are you sure you have the problem stated correctly? It's pretty easy to show the sum of the apparent weights at the top and bottom is 6mg.

 

[Carpe Mori]

yes problem is state correctly and do tell how maybe I am just over thinking it.