Question

pre - and post - collision information is shown. identify the collision parameters that are consistent with the indicated change in momentum.
initial state
p = 12 kg*m/s
6 kg
collision parameters
final state
p = 36 kg*m/s
6 kg
tap an option below to select or change an answer
(a + sign indicates a rightward direction; a - sign indicates a leftward direction.)
f = +3 n,
δt = 2 s
f = +1 n,
δt = 4 s
f = +8 n,
δt = 6 s
f = +12 n,
δt = 2 s
f = +2 n,
δt = 6 s

Explanation:

Step1: Calculate change in momentum

The initial momentum $p_i = 12\ kg\cdot m/s$ and the final momentum $p_f=36\ kg\cdot m/s$. The change in momentum $\Delta p=p_f - p_i$. So, $\Delta p=36 - 12=24\ kg\cdot m/s$.

Step2: Use impulse - momentum theorem

The impulse - momentum theorem states that $J=\Delta p = F\Delta t$. We need to check each option of $F$ and $\Delta t$ to see which one gives $F\Delta t = 24\ N\cdot s$.

Option 1:

For $F = + 3\ N$ and $\Delta t=2\ s$, $F\Delta t=(3\ N)\times(2\ s)=6\ N\cdot s$.

Option 2:

For $F = + 1\ N$ and $\Delta t = 4\ s$, $F\Delta t=(1\ N)\times(4\ s)=4\ N\cdot s$.

Option 3:

For $F = + 8\ N$ and $\Delta t=6\ s$, $F\Delta t=(8\ N)\times(6\ s)=48\ N\cdot s$.

Option 4:

For $F = + 12\ N$ and $\Delta t=2\ s$, $F\Delta t=(12\ N)\times(2\ s)=24\ N\cdot s$.

Option 5:

For $F = + 2\ N$ and $\Delta t=6\ s$, $F\Delta t=(2\ N)\times(6\ s)=12\ N\cdot s$.

Answer:

$F = + 12\ N,\Delta t = 2\ s$