Question

newtons second law of motion states that the acceleration of an object is dependent on the objects mass and the amount of force applied to the object. the table shows data from an investigation of newtons second law. which statement describes the pattern established in the data included in the chart? a doubling of the net force increases acceleration 4 times when the objects mass is constant. a doubling of the net force decreases acceleration 2 times when the objects mass is constant. a doubling of the mass decreases the acceleration of the object by half when the net force is constant. a doubling of the mass increases the acceleration of the object 2 times when the net force is constant. clear my selection

Explanation:

Step1: Recall Newton's second - law formula

Newton's second - law is $F = ma$, where $F$ is the net force, $m$ is the mass, and $a$ is the acceleration. We can rewrite it as $a=\frac{F}{m}$.

Step2: Analyze the effect of changing mass and force

When the mass $m$ is constant, $a$ is directly proportional to $F$. That is, if $F$ doubles, $a$ doubles. When the force $F$ is constant, $a$ is inversely proportional to $m$. That is, if $m$ doubles, $a$ is halved.

1. In the first two rows of the table, the net force $F = 16$ N is constant. When the mass changes from $m_1 = 4$ kg to $m_2=2$ kg (mass is halved), the acceleration changes from $a_1 = 4$ m/s² to $a_2 = 8$ m/s² (acceleration doubles).
2. In the last two rows of the table, the net force $F = 8$ N is constant. When the mass changes from $m_3 = 4$ kg to $m_4 = 2$ kg (mass is halved), the acceleration changes from $a_3 = 2$ m/s² to $a_4 = 4$ m/s² (acceleration doubles).
3. In the first and third rows of the table, the mass $m = 4$ kg is constant. When the net force changes from $F_1 = 16$ N to $F_3 = 8$ N (force is halved), the acceleration changes from $a_1 = 4$ m/s² to $a_3 = 2$ m/s² (acceleration is halved).
4. In the second and fourth rows of the table, the mass $m = 2$ kg is constant. When the net force changes from $F_2 = 16$ N to $F_4 = 8$ N (force is halved), the acceleration changes from $a_2 = 8$ m/s² to $a_4 = 4$ m/s² (acceleration is halved).

A doubling of the net force increases acceleration 2 times when the object's mass is constant.

Answer:

A doubling of the net force increases acceleration 2 times when the object's mass is constant.