Whats normal force at top/bottom of loop

[bfusco]

Homework Statement

The small mass m sliding without friction along the looped track shown in the figure is to remain on the track at all times, even at the very top of the loop of radius r.

http://session.masteringphysics.com/problemAsset/1057653/6/GIANCOLI.ch08.p090.jpg

A)In terms of the given quantities, determine the minimum release height h.
B)If the actual release height is 3h, calculate the normal force exerted by the track at the bottom of the loop.
C)f the actual release height is 3h, calculate the normal force exerted by the track at the top of the loop.

The Attempt at a Solution

A)i was easily able to solve part A, i got 2.5r
B)for this i started with energy conservation. i have that the potential energy at the beginning is equal to the kinetic energy at the bottom (3mgh=1/2mv^2, the potential energy being 3mgh because the starting height is 3h). i calculated the velocity to b v^2=6gh, which i then plugged into my centripetal force equation (ƩF=mv^2/r). N-mg=6mgh+mg, solving for N i get N=mg(6h+1/r), which is incorrect, I am instructed that the answer does not depend on height.

 

[tiny-tim]

welcome to pf!

hi bfusco! welcome to pf!

i get N=mg(6h+1/r), which is incorrect, I am instructed that the answer does not depend on height.

how did that h survive?

i thought you found what h was?​

 

[bfusco]

hi bfusco! welcome to pf!


how did that h survive?

i thought you found what h was?​

thank you tiny tim,

hm...you make a good point i guess that's what happens when you stare at a board for hours, you miss the little things. lol I am going to give that a try.

 

[bfusco]

hahahahaha it worked...i feel stupid right now. thank you for your help tiny tim