Thin ring rolling down a moving ramp

1. Mar 31, 2012

darkdraggy

1. The problem statement, all variables and given/known data
A pipe(thin ring)has a mass of 500kg and radius of 0.5m and rolls without slipping down a 300kg ramp. If the ramp is free to move horizontally(frictionless, determine the acceleration of the ramp. (angle of ramp is 30 degrees)

2. Relevant equations
Fs (static friction) = Resultant torque
Linear conservation of momentum(in horizontal axis)

3. The attempt at a solution

I am trying to get the acceleration of the ramp, i found the acceleration of the pipe using Principle of Angular momentum and I got Ap = 2.4525.

I then used the linear conservation of momentum which is 0 = (Vpcos30 - Vramp)i
then i differentiated both sides to get 0.866Ap - Aramp = 0 (cos30 = 0.866) which I then used to attempt to get Aramp. But my answer turned out to be wrong. What am i doing wrong here? any help? the solution in my book is Aramp = 1.7336

2. Mar 31, 2012

tiny-tim

welcome to pf!

hi darkdraggy! welcome to pf!
erm

masses!

3. Mar 31, 2012

darkdraggy

hello! i did use them in my equation but i did not get a correct answer.