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Conservation of Momentum in Two Dimensions

Apply component vectors to solve two dimensional collision problems

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Oh no!! Another accident!!

Why do vehicles crash the way they do?

License: CC BY-NC 3.0

The aftermath of the truck-car collision. [Figure1]

You are a pedestrian at a corner of an intersection. You see a car coming in from behind driving at 200 mph, and a truck coming in from the right driving at 120 mph. When they crash into each other, you notice that their overall combined speed is different.

A one-dimensional collision can be exemplified by the following equation using momentum:

m1v1 + m2v2 = (m1 + m2)vf

According to the equation, two masses are moving before the collision and a combined clump is moving afterwards. Therefore, it illustrates a two-car crash.

We always assume conservation of momentum. This means that the sum of the momentum of the two vehicles before the collision is the same as that of the momentum of the combined vehicle clump. Given that there is no net external force in the two-vehicle system, answer the following questions.

Creative Applications

1. How do you explain the motion of the vehicle collision using the equation? (Hint: there are two directions, so there must be two equations involved)

2. If you were to add a third vehicle in this collision, how would it affect the overall speed of the combined mass of vehicles? (Assume that the third vehicle is at rest initially)

3. Try this on your own. Get yourself two remote-control toy vehicles and have them crash into each other at an angle, observe what happens.  

Image Attributions

  1. [1]^ License: CC BY-NC 3.0

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