What Calculations Determine Roller Coaster Dynamics on a Vertical Track?

[dr2112]

Homework Statement

roller coaster traverses a vertical circular track.
a)what speed must car have to make it over the top w/o leaving the track? assume it is not attached to track.
b)what will speed be at bottom?
c)what will normal force on passenger be at the bottom of loop if radius is 14.5m?
d)at the top?

Homework Equations

a) EF=ma
n-mg=ma2
n=0 at top
b)Etop=1/2mv2(top)+mgh

The Attempt at a Solution

a) v=square root of (rg)
b)1/2mrg+mg(2*3.14) =2.5mgr
c)?
d)?

 

[alphysicist]

Hi dr2112,

Homework Statement

roller coaster traverses a vertical circular track.
a)what speed must car have to make it over the top w/o leaving the track? assume it is not attached to track.
b)what will speed be at bottom?
c)what will normal force on passenger be at the bottom of loop if radius is 14.5m?
d)at the top?

Homework Equations

a) EF=ma
n-mg=ma2
n=0 at top
b)Etop=1/2mv2(top)+mgh

The Attempt at a Solution

a) v=square root of (rg)
b)1/2mrg+mg(2*3.14) =2.5mgr

The first term (1/2 mrg) looks right for the kinetic energy at the high point. What do the other two terms represent, and how did you get those numeric values?

c)?

Do the same thing for part c that you did in part a--use Newton's law for the forces.

d)?

You've already answered this in the working for part a.