Final answer:
Filling a 12.0-gallon gas tank, which equals approximately 45.42 liters, increases the weight of a car by about 334.27 newtons, calculated by converting gallons to liters, finding mass with the density of gasoline, and applying the acceleration due to gravity.
Step-by-step explanation:
The question relates to the increase in weight of a car due to the addition of gasoline to the fuel tank. The weight of the gasoline can be calculated using its density and the volume it occupies. The density of gasoline is approximately 0.75 kg/L. One gallon is equivalent to 3.78541 liters, so a 12.0-gallon gasoline tank can hold about 45.42 liters (12.0 gal × 3.78541 L/gal). Multiplying the volume by the density gives us the mass of the gasoline: 45.42 L × 0.75 kg/L equals approximately 34.07 kg.
Weight is the force exerted by gravity on a mass. Since the acceleration due to gravity is approximately 9.81 meters per second squared (m/s²), we can calculate the increase in weight by multiplying the mass by this acceleration. The increase in weight (in newtons) can be found by multiplying the mass of the gasoline (34.07 kg) by the acceleration due to gravity (9.81 m/s²). This results in an increase of about 334.27 newtons.