A motorized winch is used to lift a crate of mass \(M\) vertically. In the first phase of the motion, the winch accelerates the crate upward from rest with a constant acceleration \(a = g\), where \(g\) is the acceleration due to gravity. At the instant the crate reaches a speed \(v\), the winch immediately adjusts its output so that the crate continues to move upward at that constant speed \(v\). Let \(P_1\) be the instantaneous power delivered by the winch to the crate at the moment it reaches speed \(v\) while still accelerating. Let \(P_2\) be the power delivered by the winch while the crate is moving at the constant speed \(v\).

What is the ratio \(\dfrac{P_1}{P_2}\)?