Simple Nature - Light and Matter

c / Bullets are dropped and shot at the same time.We call these the x, y, and z components of the velocity and themomentum.There is both experimental and theoretical evidence that thex, y, and z momentum components are separately conserved, andthat a momentum transfer (force) along one axis has no effect onthe momentum components along the other two axes. On page89, for example, I argued that it was impossible for an air hockeypuck to make a 180-degree turn spontaneously, because then in theframe moving along with the puck, it would have begun movingafter starting from rest. Now that we’re working in two dimensions,we might wonder whether the puck could spontaneously make a 90-degree turn, but exactly the same line of reasoning shows that thiswould be impossible as well, which proves that the puck can’t tradex-momentum for y-momentum. A more general proof of separateconservation will be given on page 214, after some of the appropriatemathematical techniques have been introduced.As an example of the experimental evidence for separate conservationof the momentum components, figure c shows correct andincorrect predictions of what happens if you shoot a rifle and arrangefor a second bullet to be dropped from the same height at exactlythe same moment when the first one left the barrel. Nearly everyoneexpects that the dropped bullet will reach the dirt first, andAristotle would have agreed, since he believed that the bullet hadto lose its horizontal motion before it could start moving vertically.In reality, we find that the vertical momentum transfer between theearth and the bullet is completely unrelated to the horizontal momentum.The bullet ends up with p y < 0, while the planet picksup an upward momentum p y > 0, and the total momentum in they direction remains zero. Both bullets hit the ground at the sametime. This is much simpler than the Aristotelian version!The Pelton waterwheel example 52⊲ There is a general class of machines that either do work on agas or liquid, like a boat’s propeller, or have work done on them188 Chapter 3 Conservation of Momentum