Classical Mechanics: A professor–student collaboration by Mario Campanelli

Author:Mario Campanelli
Language: eng
Format: epub, mobi
ISBN: 9780750326902
Publisher: IOP Publishing
Published: 2020-08-05T00:00:00+00:00

which is along the line of the centres (you can see this clearly from the lab view of the collision in figure 6.8). Notice from equation (6.38) that is along the same direction as , i.e. along the centre line of ball 2 in figure 6.8.

Figure 6.8. Left: collision as viewed from the laboratory frame of reference. Right: centre lines of the two colliding balls.

The impulse on ball one, due to Newton’s third law, will be

such that

Notice how ball 1 emerges from the collision at an angle θ as shown in figure 6.8. Now let us change the frame of reference and look at the angles from the centre of mass point of view. In this frame of reference the final velocities need to be in opposite directions such that the deflection angle, , of both balls is the same. This is shown in figure 6.9.

Figure 6.9. Representation of the velocities and respective angles from the centre of mass frame of reference.

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