Thin ring rolling down a moving ramp

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    Ramp Ring Rolling
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A thin ring with a mass of 500kg and a radius of 0.5m rolls down a frictionless ramp with a mass of 300kg at a 30-degree angle. The user initially calculated the ring's acceleration using angular momentum principles but found discrepancies when applying linear momentum conservation to determine the ramp's acceleration. Despite incorporating mass into the equations, the user received an incorrect result. The correct acceleration of the ramp, as per the book, is 1.7336. Assistance is requested to identify the error in the calculations.
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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
 
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welcome to pf!

hi darkdraggy! welcome to pf! :smile:
darkdraggy said:
I then used the linear conservation of momentum which is 0 = (Vpcos30 - Vramp)i

erm :redface: …

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

help anyone please? :(
 
Last edited:
darkdraggy said:
hello! i did use them in my equation but i did not get a correct answer.

help anyone please? :(


anybody can help?
 

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