Question

1. a train locomotive with a mass of 22000 kg moves east with a velocity of 4.0 m/s which collides and connects with a passenger car with a mass of 1.8×10⁴ kg which is not moving, both move off together at 2.2 m/s. prove this is a closed system and momentum is conserved. before collision after collision 2.2×10⁴ kg 1.8×10⁴ kg 2.2×10⁴ kg 1.8×10⁴ kg v₁ = 4.0 m/s v₂ = 0.0 m/s v₃ = 2.2 m/s initial (before the collision) final (after the collision) mass of locomotive a 22000 kg 22000 kg velocity of locomotive a 4 m/s 2.2 m/s mass of locomotive b 18000 kg 18000 kg velocity of locomotive b 0 m/s 2.2 m/s total momentum 88000 kg·m/s? e. assuming this is a closed system, what is the total final momentum of the locomotive - train system?____ f. is momentum conserved in this system? how do you know? g. is this an open or closed system? how do you know?

Explanation:

Step1: Calculate total final momentum

The total mass after collision is $m = 22000 + 18000=40000$ kg and the velocity $v = 2.2$ m/s. Using the formula $p=mv$, we have $p=(22000 + 18000)\times2.2$.
$p = 40000\times2.2=88000$ kg·m/s

Step2: Check momentum conservation

Initial momentum of locomotive A is $p_{A1}=22000\times4 = 88000$ kg·m/s, and initial momentum of locomotive B is $p_{B1}=18000\times0 = 0$ kg·m/s. So total initial momentum $p_1=p_{A1}+p_{B1}=88000$ kg·m/s. The total final momentum $p_2 = 88000$ kg·m/s. Since $p_1=p_2$, momentum is conserved.

Step3: Determine system type

A closed - system is one where there is no external force acting on the system. In this case, no external forces in the horizontal direction are mentioned during the collision. So we assume there is no external horizontal force, and it is a closed system.

Answer:

E. 88000 kg·m/s
F. Momentum is conserved. The total initial momentum ($88000$ kg·m/s) is equal to the total final momentum ($88000$ kg·m/s).
G. It is a closed system. There is no mention of external forces acting on the system during the collision, so we assume no external horizontal force acts on the train - car system.