Calculate the airplane's acceleration

[ConfusedMonkey]

Homework Statement

Your airplane is caught in a brief, violent downdraft. To your amazement, pretzels rise vertically off your seatback tray, and you estimate their upward acceleration relative to the plane at $2 \hspace{0.1cm} m/s^2$. What's the plane's downward acceleration?

Homework Equations

The Attempt at a Solution

I don't think I need help with the math, but I do need help understanding what's going on here. I figure that we need to focus on the plane and not the pretzels because if we choose the reference frame to be inside of the airplane, then it isn't an inertial reference frame and so Newton's laws are no longer valid, correct?

So I figure that if the plane were to accelerate downward slowly, the pretzels would stay put, but if the plane were to accelerate downward very quickly, then the pretzels would jump up off of the tray. Since the pretzel's acceleration is $2 \hspace{0.1cm} m/s^2$, then I need to find the maximum downward acceleration the plane can undergo without the pretzels jumping up, and I need to subtract $2$ from that (subtract instead of add because downward acceleration is negative). I just can't figure out how to get that number.

 

[FactChecker]

In free fall (acceleration of 1g down), what would happen?

PS. A lot of coordinate systems make acceleration down positive, so check what it is in the coordinate system you have.

 

[No1_129848]

You probably saw examples about elevators and the "change in weight" they can cause, you can also visualize what happens by just having a pen on top of your hand and then quickly moving your hand down, the pen won't catch up with your hand and it will "float" upwards if your frame of reference is actually your hand.

 

[ConfusedMonkey]

In free fall (acceleration of 1g down), what would happen?

PS. A lot of coordinate systems make acceleration down positive, so check what it is in the coordinate system you have.

If it were in free fall, the pretzels would still be on the tray because only gravity would be acting on the plane and on the pretzels. But there is nothing in the question to indicate free fall. From what I see, the forces on the plane are gravity, the force of the air which pushes the plane up, and the downward wind draft which is causing turbulence.

EDIT: If it were in free fall, the pretzels would remain on the tray since they too would also be in free fall, but if the plane all of a sudden started accelerating downward, then the pretzels would keep their initial acceleration of -9.8 m/s^2. This must mean that for the pretzels to appear as if they are rising with an acceleration of 2 m/s^2, then the plane must be accelerating downward at 9.8 + 2 = 11.8 m/s^2. But still, this is assuming it is in free fall, as I mentioned above, there are other forces to take into consideration.

EDIT 2: If the plane is accelerating downward, obviously the net force points downward. As long as the acceleration that the plane moves downward at is 9.8 m/s^2 or less, then the pretzels will fall at the same rate and thus NOT come off of the tray. However, as soon as the planes downward acceleration passes this point, then the pretzels MUST start to "rise". The fact that the pretzels appear to accelerate upward at 2 m/s^2 means thus means that the plane must be accelerating downward at 11.8 m/s^2. I think I've got it!

 

[No1_129848]

Yes, that should be the correct thought process