Final answer:
The question is about calculating the normal force exerted on the wall of a glass bottle by the juice inside, due to expansion from temperature increase, using the given bulk modulus.
The normal force will help determine the bottle's ability to withstand internal pressure without breaking.
Step-by-step explanation:
The question involves calculating the normal force exerted by a fluid within a glass bottle due to the fluid's expansion when subjected to temperature changes. To solve this problem, you need to understand the concepts of bulk modulus and pressure.
The bulk modulus is a measure of a material's resistance to uniform compression. For a fluid undergoing a small volume change ∆V within a container with initial volume V₀, the formula for the pressure increase (∆P) is ∆P = -B*(∆V/V₀), where B is the bulk modulus. In this case, the volume change is 0.2% of the available space, and the bulk modulus of the juice is given as 1.8×10¹ N/m².
Using these pieces of information, we can calculate the pressure exerted by the juice as a result of its expansion. The normal force per unit area (pressure) experienced by the bottle due to this pressure can determine whether the bottle is likely to break or withstand the internal force.