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Find the range of acceleration so that the drums won't fall

Problem:

oil_drums.png

Attempt: I tried to solve the range by listing out the newton's 2nd laws of each drum
1.png


and from the equations of the drum 2, I get
N1_N2.png


Since drum 2 must stay on the bottom drums, so it will not fly up, thus
upper_bound.png


I got the upper bound of the acceleration, but I don't know if it is correct.


My question:
Although I got the seemingly correct upper bound of the acceleration, but I don't know how I can get the lower bound of the acceleration?
 

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haruspex

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got the seemingly correct upper bound of the acceleration, but I don't know how I can get the lower bound of the acceleration?
Each bound corresponds to the system falling apart. In which two ways can that happen? What can you say about the normal forces in those two cases?
 
Each bound corresponds to the system falling apart. In which two ways can that happen? What can you say about the normal forces in those two cases?
Well, I think there are two cases, one is for the upper bound I solved(corresponds to the top drum flying up); the other case is for the lower bound(it corresponds to the situation when the top drum is falling down, i.e. N_1 and N_2 are not enough to support the top drum.)
 

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