Final answer:
The buoyancy force exerted on a 1-liter bottle submerged 1/4 of the way into water is calculated using Archimedes' Principle, with the result being 2.4525 newtons.
Step-by-step explanation:
The subject of the question is Physics, specifically a concept related to buoyancy and Archimedes' Principle. When an object is submerged in a fluid, it experiences an upward force called the buoyant force. According to Archimedes' Principle, this force is equal to the weight of the fluid displaced by the object.
For a 1-liter bottle that is submerged 1/4 of the way into water, we can calculate the buoyant force by finding the volume of the water displaced, which in this case is 0.25 liters or 0.25 kg (since 1 liter of water has a mass of approximately 1 kg). The buoyant force would then be this mass multiplied by the acceleration due to gravity (9.81 m/s²).
To perform the calculation, the formula for buoyant force (Fb) is:
Fb = mdisplaced × g
where mdisplaced is the mass of the displaced water and g is the acceleration due to gravity. Therefore, the buoyant force exerted on the bottle would be:
Fb = 0.25 kg × 9.81 m/s²
Fb = 2.4525 N