Question

by rearranging newtons second law, we find that the net force acting on an object is equal to all of these quantities.
sum vec{f}=m vec{a}=m \frac{delta vec{v}}{delta t}=\frac{delta m vec{v}}{delta t}=\frac{delta vec{p}}{delta t}
consider a system of two objects. the objects interact with each other via forces, but they experience no unbalanced forces from outside the system.
select the quantities that must be equal in magnitude for both objects as they interact.
choose all answers that apply:
a the net force acting on each object ((sum vec{f}))
b the amount of time that each object experiences a force ((delta t))
c the change in each objects momentum ((delta vec{p}))
d the change in each objects velocity ((delta vec{v}))

Explanation:

• Option A: According to Newton's third law, when two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction. So, the net force acting on each object (due to the interaction) has the same magnitude.
• Option B: The interaction between the two objects is simultaneous. So, the time interval \(\Delta t\) for which the force acts on each object is the same.
• Option C: From \(\sum\vec{F}=\frac{\Delta\vec{p}}{\Delta t}\), since \(\sum\vec{F}\) (due to interaction) has the same magnitude and \(\Delta t\) is the same for both objects, \(\Delta\vec{p}\) (change in momentum) has the same magnitude for both objects.
• Option D: Using \(\Delta\vec{p} = m\Delta\vec{v}\), if the masses of the two objects \(m_1

eq m_2\), then even if \(\vert\Delta\vec{p}_1\vert=\vert\Delta\vec{p}_2\vert\), \(\vert\Delta\vec{v}_1\vert
eq\vert\Delta\vec{v}_2\vert\) (because \(\vert\Delta\vec{v}\vert=\frac{\vert\Delta\vec{p}\vert}{m}\)).

Answer:

A. the net force acting on each object \((\sum\vec{F})\), B. the amount of time that each object experiences a force \((\Delta t)\), C. the change in each object's momentum \((\Delta\vec{p})\)