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## Homework Statement

A mass of 100kg is h meters high on a track that extends into a loop that has a radius of 20m. Assume track is frictionless. I need to find minimum height for the mass to make it around the loop without falling off or going backwards.

## Homework Equations

Conservation of Energy:

K_1+U_2=K_2+U_2

v=sqrt(2gh)

Force:

F=ma

F=mg

Centripetal Force:

(mv^2)/r=F

## The Attempt at a Solution

This may be right, i only need someone to check my work in case im incorrect. So, from K_1+U_1=K_2+U_2 i get K=U

From there i have 1/2mv^2=mgh

masses cancel so v^2=2gh

from there i find centripetal force = (mv^2)/r=F

F=mg=(mv^2)/r

masses again cancel so i find that g=(v^2)/r

I replace v^2 with 2gh so i find that g=2gh/r

g's cancel so i find that h=r/2 plug in for r: h = 20/2=10meters.

Can someone verify that im correct? thanks in advance!