Question

A dart gun is used to fire two rubber darts with different but unknown masses, m1 and m2. The gun exerts the same constant force on each dart, but its magnitude F is unknown. The magnitudes of the accelerations of both darts, a1 and a2, respectively, are measured. Which of the following can be determined from these data?

Options:
a. The ratio of m1 to m2
b. The magnitude of F
c. The ratio of a1 to a2
d. The individual masses m1 and m2

Answer 1

Using Newton's second law and knowing that the same force acts on both darts, we can determine the ratio of the masses of the darts from the inverse ratio of their accelerations; m1/m2 = a2/a1. No other measurements, such as the magnitude of force or the individual masses, can be deduced.

Step-by-step explanation:

The question involves analyzing the motion of two darts fired from a dart gun and determining what can be deduced from the given data, which includes the magnitude of acceleration for each dart, but not the force exerted or the masses of the darts. According to Newton's second law, force (F) is equal to mass (m) times acceleration (a), which is represented by the equation F = ma. Since the same constant force is exerted on both darts, we can set up the following proportional relationship:

For dart 1: F = m1 * a1
For dart 2: F = m2 * a2
If the force is constant and the same for both darts, we can infer that the ratio of the masses is inversely proportional to the ratio of their accelerations. This relationship can be shown as m1/m2 = a2/a1, which means we can determine the ratio of m1 to m2 from the measured accelerations. However, we cannot determine the magnitude of F, the individual masses m1 and m2, or the ratio of a1 to a2 without additional information.