Rolling down a ramp - find acceleration

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serverxeon
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Diagram of a thin ring labelled P rolling down a wedge-shaped ramp inclined at 30 degrees on wheels, with a point labelled A marked inside the ramp, and printed problem text about a 500 kg ring and 300 kg ramp.


Here are the few equations i set up... which ultimately led to a wrong answer.
(In my solution, subscripts A refers to the ramp, B refers to the rolling pipe)

Handwritten free-body diagrams with equations for a cylinder rolling on a movable ramp at 30 degrees: forces N, F_f, m_B g, and ramp forces N_f, m_A g, with equations including m_A a_A = N_p sin30 - F_f cos30.


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I have a feeling that the acceleration if pipe A isn't simply downwards at 30deg.
Cos the ramp is rolling away, so the angle is relative to the ramp.

But I have no idea how to set up the required equations to correct this.
Any pointers?
 
hi serverxeon! :smile:
serverxeon said:
I have a feeling that the acceleration if pipe A isn't simply downwards at 30deg.
Cos the ramp is rolling away, so the angle is relative to the ramp.

relative accelerations are vectors (like relative velocities or relative positions), and so they add like vectors :wink: