TBR Physics Ch. 7, Q#2: Stress and Strain on Hulls

[Majik]

2. Which of the following describes changes in volume in the hull of an airplane, as the plane takes off from and then returns to the runway?

Answer: B - An INCREASE in hull volume, followed by a DECREASE.

I chose this answer because it makes intuitive sense, but I can't reason this out using the equation:

deltaP = -(B)(deltaV / original volume); 'B' is the bulk modulus (a constant up to a certain limit).

It makes sense that as you rise up, the pressure decreases and the change in pressure would be an overall negative value. However, I'm a little confused with the variables in this equation:

1.) How does a negative change in pressure relate to the change in volume of the object?

2.) Also, the pressure decreases by some fraction so shouldn't the change in volume decrease equivalently by the same amount for B to remain at its constant value?

I'm going to venture a guess and say that the negative change in pressure means a positive change in volume (increase in volume) since decreasing pressure by some fraction:

(-X/Y)deltaP is proportional to the change in volume of the solid: -B (-X/Y)deltaV/V

The two negatives represent a positive change in volume. This change in volume is proportional to the magnitude the pressure decreased. If this is wrong, please let me know.

Does anyone have a better / more intuitive way to go about using this equation? If so, please share. Thanks.

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[muhali3]

I do not. But...this topic isn't tested often and when it is, the answer wouldn't require such a deep understanding of the equation, but only an intuitive understanding of the variables. I've studied with TBR, and they tend to go into much more mathematical detail than the AAMCs require. None of the questions I've seen on the AAMCs have actually required very long multi-step math.

So...I don't really have an answer to your question. I would just compare it to breathing, where negative pressure causes an increases in volume of the lungs.