Question

external unbalanced force.
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 } _ { \text { tot } } \\) )?
choose 1 answer

Explanation:

Step1: Recall the law of conservation of momentum

The law of conservation of momentum states that if there is no external un - balanced force acting on a system, the total momentum of the system \(p_{tot}\) is conserved, i.e., \(p_{tot,i}=p_{tot,f}\).

Step2: Calculate the initial total momentum

The initial momentum of object \(A\) is \(\vec{p}_{Ai}\) (non - zero, say in the positive \(x\) - direction) and the initial momentum of object \(B\) is \(\vec{p}_{Bi} = 0\). So, \(p_{tot,i}=\vec{p}_{Ai}+\vec{p}_{Bi}=\vec{p}_{Ai}\) (in the direction of \(\vec{p}_{Ai}\)).

Step3: Analyze the options

Since there is no external un - balanced force, the total momentum of the system before and after the interaction is the same. The initial total momentum is non - zero and in the direction of \(\vec{p}_{Ai}\) (assuming \(\vec{p}_{Ai}\) is in the right - hand direction as per the standard in such problems where the arrow is drawn to the right for \(\vec{p}_{Ai}\) in the initial condition).

Answer:

D.