Rope Sliding on Double Ramp

A \(\SI{1}{\kilo\gram}\) rope of length \(\SI{1.5}{\meter}\) slides down a frictionless double ramp in the shape of an equilateral triangle, as shown in the diagram above. At time \(t = 0\), the rope is at rest with \(\SI{1}{\meter}\) of its length on the right side of the ramp.

How much time (in seconds, to 3 decimal places) elapses before all of the rope is on the right side?

\(\)
Details and Assumptions:

  • The downward gravitational acceleration is \(\SI[per-mode=symbol]{10}{\meter\per\second\squared}.\)
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