Question

object c and object d are interacting with each other. both objects are also interacting with other objects. based on this information, which quantities must be equal in magnitude at all times? choose all answers that apply: a the force (f) from c on d and the force from d on c b the net force (σf) on c and the net force on d c the acceleration (a) of c and the acceleration of d d the velocity (v) of c and the velocity of d

Explanation:

Step1: Analyze Newton's third law

According to Newton's third law, when two objects interact, the force exerted by object C on object D ($F_{C
ightarrow D}$) and the force exerted by object D on object C ($F_{D
ightarrow C}$) are an action - reaction pair. So, $F_{C
ightarrow D}=-F_{D
ightarrow C}$, which means their magnitudes are equal, $|F_{C
ightarrow D}| = |F_{D
ightarrow C}|$.

Step2: Analyze net force

The net force on an object is the vector sum of all forces acting on it. Since objects C and D are also interacting with other objects, the net force on C ($\sum\vec{F}_C$) and the net force on D ($\sum\vec{F}_D$) are not necessarily equal. For example, if object C has an additional force from a third object and object D does not, $\sum\vec{F}_C
eq\sum\vec{F}_D$.

Step3: Analyze acceleration

From Newton's second law $\vec{F} = m\vec{a}$, $\vec{a}=\frac{\vec{F}}{m}$. Even if the forces between C and D are equal in magnitude (from step 1), if the masses of C ($m_C$) and D ($m_D$) are different ($m_C
eq m_D$), and the net forces are different (from step 2), $a_C=\frac{\sum\vec{F}_C}{m_C}$ and $a_D=\frac{\sum\vec{F}_D}{m_D}$ will not be equal.

Step4: Analyze velocity

Velocity $\vec{v}$ is related to acceleration and initial conditions ($\vec{v}=\vec{v}_0+\vec{a}t$). Since accelerations (from step 3) and initial velocities ($\vec{v}_{0C}$ and $\vec{v}_{0D}$) are not necessarily equal, the velocities of C and D are not necessarily equal.

Answer:

A. the force ($F$) from C on D and the force from D on C