Question

the models below represent the objects before and after they interact. the length of each momentum vector represents its magnitude.
initial (i) conditions-before interaction
final (f) conditions-after interaction
we can use the models to predict the final momentum of object a after the interaction.
what is the total momentum of the system before and after the interaction (\vec{p}_{tot})?
choose 1 answer:

Explanation:

Step1: Calculate initial total momentum

The total initial momentum \( \vec{p}_{tot,i}\) of the system is the sum of the initial momenta of object \(A\) and object \(B\). Given \( \vec{p}_{Ai}\) (non - zero, say magnitude \(p_{Ai}\)) and \( \vec{p}_{Bi}=0\), so \( \vec{p}_{tot,i}=\vec{p}_{Ai}+\vec{p}_{Bi}=\vec{p}_{Ai}\) (direction is the same as \( \vec{p}_{Ai}\), which is to the right as per the initial - condition diagram).

Step2: Apply law of conservation of momentum

According to the law of conservation of momentum \( \vec{p}_{tot,i}=\vec{p}_{tot,f}\). Since there are no external forces acting on the system (implicit in momentum - conservation problems of this type, as we are just looking at the interaction between \(A\) and \(B\)), the total momentum of the system before and after the interaction is the same.

Answer:

E.