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

$F = ma$ (where $F$ is net force, $m$ is mass, $a$ is acceleration)

Step2: Analyze first two rows

When $m = 4$ kg and $F = 16$ N, $a=\frac{F}{m}=\frac{16}{4}=4$ m/s². When $m = 4$ kg and $F = 8$ N, $a=\frac{F}{m}=\frac{8}{4}=2$ m/s². Doubling $F$ from 8 N to 16 N doubles $a$ from 2 m/s² to 4 m/s².

Step3: Analyze last two rows

When $m = 2$ kg and $F = 8$ N, $a=\frac{F}{m}=\frac{8}{2}=4$ m/s². When $m = 2$ kg and $F = 16$ N, $a=\frac{F}{m}=\frac{16}{2}=8$ m/s². Doubling $F$ from 8 N to 16 N doubles $a$ from 4 m/s² to 8 m/s². In general, when $m$ is constant, $a\propto F$. If $F$ doubles, $a$ doubles. But if we consider the relationship between the first and last rows where $F$ doubles from 8 N to 16 N and $m$ is halved from 4 kg to 2 kg, from $a=\frac{F}{m}$, the new acceleration is 4 times the old one.

Answer:

A doubling of the net force increases acceleration 4 times when the object's mass is constant.