Thin ring rolling down a moving ramp

[darkdraggy]

Homework Statement

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)

Homework Equations

Fs (static friction) = Resultant torque
Linear conservation of momentum(in horizontal axis)

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

 

[tiny-tim]

welcome to pf!

hi darkdraggy! welcome to pf!

I then used the linear conservation of momentum which is 0 = (Vpcos30 - Vramp)i

erm …

masses! ​

 

[darkdraggy]

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

help anyone please? :(

 

[darkdraggy]

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

help anyone please? :(

anybody can help?