Question

worksheet #4 - collisions in 2 - d

1. how does understanding momentum conservation help in accident analysis? discuss both the benefits and limitations of using momentum conservation in this context.
2. a large locomotive with a mass 4 times that of the smaller, motionless railroad car collides and couples together. what is their combined velocity after the collision?

Explanation:

Step1: Apply the law of conservation of momentum

The law of conservation of momentum states that \(p_{initial}=p_{final}\). The initial momentum is the momentum of the locomotive only since the railroad car is motionless. So, \(p_{initial} = 4m\times5\) (where \(m\) is the mass of the smaller car and \(4m\) is the mass of the locomotive). The final mass is \(4m + m=5m\), and let the final velocity be \(v\). Then \(p_{final}=(4m + m)v\).

Step2: Solve for \(v\)

Set \(p_{initial}=p_{final}\), so \(4m\times5=(4m + m)v\). Substitute \(p_{initial}=20m\) and \(p_{final} = 5mv\). Then \(20m=5mv\). Divide both sides by \(5m\) (assuming \(m
eq0\)). We get \(v = 4\) km/hr.

Answer:

The combined velocity after the collision is \(4\) km/hr.