Question

pre - and post - collision information is shown. identify the collision parameters that are consistent with the indicated change in momentum.
initial state
v = 4 m/s
5 kg
collision parameters
final state
v = 12 m/s
5 kg
tap an option below to select or change an answer.
(a + sign indicates a rightward direction; a - sign indicates a leftward direction.)
impulse = +16 n·s
f = +12 n, δt = 4 s
δp = +8 kg·m/s
f = +60 n, δt = 3.0 s
δp = +40 kg·m/s
check answer

Explanation:

Step1: Recall the impulse - momentum theorem

The impulse - momentum theorem states that $J=\Delta p$, where $J$ is the impulse and $\Delta p$ is the change in momentum. Also, impulse $J = F\Delta t$, where $F$ is the average force and $\Delta t$ is the time interval.

Step2: Calculate the initial momentum

The initial momentum $p_i=mv_i$, where $m = 5\ kg$ and $v_i=4\ m/s$. So, $p_i=5\times4=20\ kg\cdot m/s$.

Step3: Calculate the final momentum

The final momentum $p_f=mv_f$, where $m = 5\ kg$ and $v_f = 12\ m/s$. So, $p_f=5\times12 = 60\ kg\cdot m/s$.

Step4: Calculate the change in momentum

$\Delta p=p_f - p_i=60 - 20=40\ kg\cdot m/s$.

Step5: Check the impulse - momentum combinations

We know that $J=\Delta p$. For $F = + 60\ N$ and $\Delta t=3.0\ s$, $J=F\Delta t=60\times3=180\ N\cdot s$. For $F = + 12\ N$ and $\Delta t = 4\ s$, $J=F\Delta t=12\times4 = 48\ N\cdot s$. The impulse $J=+16\ N\cdot s$ is not equal to $\Delta p$. The correct combination is when $\Delta p=+40\ kg\cdot m/s$.

Answer:

$\Delta p=+40\ kg\cdot m/s$