Elastic Collisions

If two objects collide, one stationary and one moving, the resulting velocity of the two objects is given by:

What happens if one mass is much larger than the other? Say m2 >>> m1. We can use the same equation as before but we might as well ignore the very tiny m1 values. This gives us:

What if both objects are moving though? For example, a large mass m2 is struck by a little mass m1. →BANG!← We can go into a moving frame of reference. For instance, if we are standing on the big mass, our speed of reference becomes the velocity of big mass. Now the little mass is moving at a velocity relative to our frame of reference i.e. –(v+V).

Once we solve for the velocities, we can go back to the ground frame of references, by subtracting what we did in the first place to get into the moving frame of reference.

This principle, how a little mass colliding with a big mass manages to pick up so much extra velocity from the big mass is called “Sling shot” it is used commonly to launch space probes at a faster speed into deep space.

We should be able to use this principle to calculate the height of a tennis ball dropped at the same time as a basket ball and striking the basket ball as it hits the ground. (The tennis ball flies off to great heights.)

Now we switched to talking about the forces acting on a tennis ball as it is struck by a racket. If you plot this force, it has a large spike in force, for a short amount of time. So this is easier almost to calculate using change in momentum.

Now, what happens if we move into two dimensions? Consider the law of conservation of momentum as a queue ball strikes a pool ball and the two balls move off on different trajectories. The vector for conservation of momentum can be broken into it’s component parts.

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One Response to Elastic Collisions

  1. Dad

    In the B-ball frame of reference after the bounce, I see the T-ball moving towards me at 2V, it hits and moves away from me at 2V. To get back to the observer frame of reference, I need to add an upward V to the system so 2V+V –> 3V

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