Final answer:
To determine the fraction of a 910 kg car with 3.1 m³ volume that is submerged when floating, we use the weight of the car in water to find the volume of water it displaces. We find that approximately 29.4% of the car's volume is submerged.
Step-by-step explanation:
The question asks about the fraction of a car that would be submerged when it floats, given that the car's mass is 910 kg and its interior volume is 3.1 m³. According to Archimedes' Principle, the fraction submerged is the ratio of the volume submerged to the volume of the object. The submerged volume can be calculated using the density of the fluid and the mass of the car, which tells us the weight of the fluid displaced.
Let's assume the car is floating in freshwater, with a density of approximately 1000 kg/m³. The car displaces a volume of water equal to its own weight divided by the density of the water. The mass of the car (m) is 910 kg, so the weight (W) of the car is m×g, where g is the acceleration due to gravity (9.81 m/s²). So, the weight of the displaced water is 910 kg × 9.81 m/s² = 8927.1 N.
The volume of water displaced (Vw) equals the weight of the car (W) divided by the product of the density of water (Pw) and gravity (g), that is Vw = W / (Pw × g). Plugging in the numbers, we get Vw = 8927.1 N / (1000 kg/m³ × 9.81 m/s²) = 0.910 m³. This is the volume of the car that is submerged when floating.
The fraction of the car that is submerged is therefore 0.910 m³ / 3.1 m³. The complete calculated answer is approximately 0.294, or 29.4% of the car's volume is submerged when it floats.