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 multiple choice 3 points net force (n) 16 16 8 8 mass (kg) 4 2 4 2 acceleration (m/s²) 4 8 2 4

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 case when mass is constant

When the mass $m$ is constant, $a$ is directly proportional to $F$. If the net - force $F$ doubles, from $F_1$ to $F_2 = 2F_1$, then $a_1=\frac{F_1}{m}$ and $a_2=\frac{F_2}{m}=\frac{2F_1}{m}=2a_1$. So doubling the net force increases the acceleration 2 times when the mass is constant.

Step3: Analyze the case when force is constant

When the force $F$ is constant, $a$ is inversely proportional to $m$. If the mass doubles, from $m_1$ to $m_2 = 2m_1$, then $a_1=\frac{F}{m_1}$ and $a_2=\frac{F}{m_2}=\frac{F}{2m_1}=\frac{1}{2}a_1$. So doubling the mass decreases the acceleration by half when the net force is constant.

Answer:

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