Question

table 3: net force vs mass

based on table 3, is the relationship between mass and net force directly or inversely proportional? explain with evidence from the data table.

Explanation:

Step1: Recall the formula for direct and inverse proportionality

For two variables \(x\) and \(y\), if \(y = kx\) (where \(k\) is a constant), they are directly proportional. If \(y=\frac{k}{x}\), they are inversely proportional. Here, from Newton's second law \(F = ma\), when \(a\) is constant (\(a = 2.0\ m/s^{2}\) in the table), \(F\) and \(m\) follow \(F=ma\) (similar to \(y = kx\) form).

Step2: Check the ratio of net - force to mass

For the first row: \(\frac{F}{m}=\frac{8.0\ N}{4.0\ kg}=2.0\ m/s^{2}\)
For the second row: \(\frac{F}{m}=\frac{16\ N}{8.0\ kg}=2.0\ m/s^{2}\)
For the third row: \(\frac{F}{m}=\frac{24\ N}{12\ kg}=2.0\ m/s^{2}\)
For the fourth row: \(\frac{F}{m}=\frac{32\ N}{16\ kg}=2.0\ m/s^{2}\)
For the fifth row: \(\frac{F}{m}=\frac{40\ N}{20\ kg}=2.0\ m/s^{2}\)

Since the ratio \(\frac{F}{m}\) (which is equal to acceleration \(a\)) is constant (\(a = 2.0\ m/s^{2}\)), the relationship between mass (\(m\)) and net - force (\(F\)) follows \(F=ma\) (where \(a\) is the constant of proportionality).

Answer:

The relationship between mass and net force is directly proportional. As shown in the data table, when we calculate the ratio \(\frac{F}{m}\) for each row (e.g., \(\frac{8.0}{4.0}=2.0\), \(\frac{16}{8.0}=2.0\), \(\frac{24}{12}=2.0\), \(\frac{32}{16}=2.0\), \(\frac{40}{20}=2.0\)), the ratio (which is the acceleration \(a\) from \(F = ma\)) is constant. According to the definition of direct proportionality (\(y=kx\), here \(F = ma\) with \(a\) constant), mass and net force are directly proportional.