- #1
Panphobia
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Homework Statement
A man starts riding on a frictionless roller coaster track at initial velocity v[itex]_{o}[/itex]. At point A the radius of the bend is r.
a) What is the maximum v[itex]_{o}[/itex] such that when the cart gets at point A it stays on the track?
b) Using you answer in a) what should h' be such that the cart only just makes it to point B?
Homework Equations
Ei = Ef
mv^2/r
The Attempt at a Solution
So this question was kind of bugging me, and I want to know if I got it right so for the a) part this is what I did firstly
mgh + (1/2)mv[itex]_{o}[/itex][itex]^{2}[/itex] = mg(2/3)h+1/2mv[itex]^{2}[/itex]
v = [itex]\sqrt{2gh/3 + Vo^2}[/itex]
and then since at point be its a circle and its looking for the max velocity until the normal force = 0 I did
mv^2/r = mg
v = [itex]\sqrt{rg}[/itex]
then
rg = 2gh/3 + v[itex]_{o}[/itex][itex]^{2}[/itex]
v[itex]_{o}[/itex] = [itex]\sqrt{g*(r-(2/3)h)}[/itex]THEN for b) I just used Energy again.
so
v = [itex]\sqrt{rg}[/itex]
Ei = (1/2)mrg + mg(2/3)h
Ef = mgh'
h' = r/2 + 2h/3