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 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 effect of changing mass and force

• When the net - force $F$ is constant:
• If we double the mass ($m_2 = 2m_1$), then $a_1=\frac{F}{m_1}$ and $a_2=\frac{F}{m_2}=\frac{F}{2m_1}=\frac{1}{2}a_1$. So the acceleration is halved when the mass is doubled with constant force.
• When the mass $m$ is constant:
• If we double the net - force ($F_2 = 2F_1$), then $a_1=\frac{F_1}{m}$ and $a_2=\frac{F_2}{m}=\frac{2F_1}{m}=2a_1$. So the acceleration is doubled when the net force is doubled with constant mass.
• Looking at the data in the table, when the mass is constant (e.g., mass $m = 4$ kg in the first and third rows), doubling the net force from $8$ N to $16$ N doubles the acceleration from $2$ m/s² to $4$ m/s². When the net force is constant (e.g., net force $F = 8$ N in the third and fourth rows), doubling the mass from $2$ kg to $4$ kg halves the acceleration from $4$ m/s² to $2$ m/s².

Answer:

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