Final answer:
The time of fall to reach terminal velocity for coffee filters is influenced by both the drag force and the weight of the filters.
Terminal velocity is likely to show a more linear relationship when plotted against the square of the mass, indicating that it's not inversely proportional to the weight (mg) but is affected by multiple factors.
Step-by-step explanation:
The question asks how the time of fall is related to the weight (mg) of the coffee filters' drag force. The weight mg represents the gravitational force, which is directly proportional to mass and inversely proportional to the square of the distance from the Earth (according to the law of universal gravitation).
In the case of falling coffee filters, the fall time to reach the terminal velocity is influenced by the drag force and the weight of the filters.
When drag force is constant (assuming the shape and the air resistance remains the same), and only mass varies, the terminal velocity will change with the mass of the filters. An increase in mass (mg) will result in a higher terminal velocity because the gravitational force pulling the filters down increases.
Conducting a take-home experiment by dropping coffee filters with varying numbers of layers would show that the terminal velocity squared (v²) is likely to be more linear when plotted against mass, which implies that the terminal velocity increases with the square root of the mass.
This means that although the time it takes to reach terminal velocity may differ for different masses, it is not inversely proportional to the weight (mg). Instead, it demonstrates a more complicated relationship affected by various factors including mass, gravity, and drag force.