open stax even answers - A farmer making grape juice fills a glass bottle to the brim and caps it tightly. The juice expands more than the glass when it warms up, in such a way that the volume increases by 0.2% (that is, ΔV / V0 = 2×10−3) relative to the space available. Calculate the magnitude of the normal force exerted by the juice per square centimeter if its bulk modulus is 1.8×109 N/m2 , assuming the bottle does not break. In view of your answer, do you think the bottle will survive?

A farmer making grape juice fills a glass bottle to the brim and caps it tightly. The juice expands more than the glass when it warms up, in such a way that the volume increases by 0.2% (that is, ΔV / V0 = 2×10−3) relative to the space available. Calculate the magnitude of the normal force exerted by the juice per square centimeter if its bulk modulus is 1.8×109 N/m2 , assuming the bottle does not break. In view of your answer, do you think the bottle will survive?

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open stax even answers openstax physics solutions manual A farmer making grape juice fills a glass bottle to the brim and caps it tightly the magnitude of the normal force exerted by the juice

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Sahil Khan (last edited 1 year ago)

Using the equation \Delta V = \frac{1}{B}\frac{F}{A} V_{0} gives:

\frac{F}{A} = B \frac{\Delta V}{V} = \Big(1.8 \times 10^{9} \frac{N}{m^{2}}\Big)(2 \times 10^{-3}) = 3.6 \times 10^{6}\frac{N}{m^{2}} = 4 \times 10^{2}\frac{N}{cm^{2}}

Since 1 atm = 1.013 \times 10^{5} \frac{N}{m^{2}}, the pressure is about 36 atmospheres, far greater than the average jar is designed to withstand.

So the bottle will not survive.

Qalaxia Master Bot (last edited 1 year ago)

I found an answer from www.andrews.edu

Student Solutions Manual

Chapter 4: Dynamics: Force and Newton's Laws of Motion . ... A farmer making grape juice fills a glass bottle to the brim and caps it tightly. The juice.

For more information, see Student Solutions Manual