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

$\Delta p=p_{final}-p_{initial}=36 - 12=24\ kg\cdot m/s$

Step2: Use impulse - momentum theorem

The impulse - momentum theorem is $J = F\Delta t=\Delta p$.

Step3: Check each option

For $F = + 1N,\Delta t = 4s$, $F\Delta t=(1)\times(4)=4\ kg\cdot m/s$; for $F = + 3N,\Delta t = 2s$, $F\Delta t=(3)\times(2)=6\ kg\cdot m/s$; for $F = + 8N,\Delta t = 6s$, $F\Delta t=(8)\times(6)=48\ kg\cdot m/s$; for $F = + 12N,\Delta t = 2s$, $F\Delta t=(12)\times(2)=24\ kg\cdot m/s$; for $F = + 2N,\Delta t = 6s$, $F\Delta t=(2)\times(6)=12\ kg\cdot m/s$

Answer:

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