Final answer:
Elasticity is about how substances return to their original shape after deformation. A pocket of air in a bottle of vinegar prevents breakage by allowing space for expansion when the vinegar warms up and expands more than the glass. A wire strung tightly to hold a picture is more likely to snap than one that sags because it's under more tension.
Step-by-step explanation:
The concept of elasticity in physics relates to a material's ability to return to its original shape after being deformed by external forces. When considering a bottled water scenario, the elasticity of the water itself is not primarily the concern but rather the elasticity of the bottle material. However, when considering the changes in volume due to temperature fluctuations, the water's ability to expand is crucial.
When a glass bottle full of vinegar warms up, the vinegar expands more than the glass due to having a higher coefficient of thermal expansion. This can lead to an increase in pressure inside the bottle, potentially causing the bottle to break if there is no space for the liquid to expand into. Providing a pocket of air at the top of the bottle allows the vinegar to expand without significantly increasing internal pressure, as the air is compressible and can accommodate the volume change more easily than the glass can. This prevents the breakage of the bottle.
With regard to a wire supporting a picture, if the wire is strung tightly, there is a greater risk of it snapping compared to when it is strung loosely and sags considerably. A tightly strung wire is under more tension and closer to its breaking point, whereas a sagging wire has a margin of elasticity to absorb any additional forces that may act upon it.
Stress and strain are related quantitatively in physics, where stress is the force applied per unit area, and strain is the deformation experienced by a material due to the applied stress. The similarity between the two quantities is that they both measure how materials respond to external forces, with stress focusing on the cause and strain on the effect. They are both critical components in understanding material elasticity.