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.

Explanation:

Step1: Recall Newton's second law

$F = ma$, where $F$ is net - force, $m$ is mass and $a$ is acceleration. So, $a=\frac{F}{m}$.

Step2: Analyze the effect of changing force with constant mass

If the mass $m$ is constant, and the net - force $F$ is doubled (let the initial force be $F_1$ and the new force be $F_2 = 2F_1$), then the initial acceleration $a_1=\frac{F_1}{m}$ and the new acceleration $a_2=\frac{F_2}{m}=\frac{2F_1}{m}=2a_1$.

Step3: Analyze the effect of changing mass with constant force

If the force $F$ is constant, and the mass is doubled (let the initial mass be $m_1$ and the new mass be $m_2 = 2m_1$), then the initial acceleration $a_1=\frac{F}{m_1}$ and the new acceleration $a_2=\frac{F}{m_2}=\frac{F}{2m_1}=\frac{1}{2}a_1$.

Step4: Check the data in the table

When the net - force changes from 8 N to 16 N with mass constant (4 kg), acceleration changes from 2 m/s² to 4 m/s² (doubles). When the mass changes from 2 kg to 4 kg with force constant (8 N), acceleration changes from 4 m/s² to 2 m/s² (halves).

Answer:

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