Chapter 1 Conservation of Mass - Light and Matter
Chapter 1 Conservation of Mass - Light and Matter
Chapter 1 Conservation of Mass - Light and Matter
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f / Example 1.<br />
58 <strong>Chapter</strong> 1 <strong>Conservation</strong> <strong>of</strong> <strong>Mass</strong><br />
1.1.1 Problem-solving techniques<br />
How do we use a conservation law, such as conservation <strong>of</strong> mass,<br />
to solve problems? There are two basic techniques.<br />
As an analogy, consider conservation <strong>of</strong> money, which makes it<br />
illegal for you to create dollar bills using your own inkjet printer.<br />
(Most people don’t intentionally destroy their dollar bills, either!)<br />
Suppose the police notice that a particular store doesn’t seem to<br />
have any customers, but the owner wears lots <strong>of</strong> gold jewelry <strong>and</strong><br />
drives a BMW. They suspect that the store is a front for some kind<br />
<strong>of</strong> crime, perhaps counterfeiting. With intensive surveillance, there<br />
are two basic approaches they could use in their investigation. One<br />
method would be to have undercover agents try to find out how<br />
much money goes in the door, <strong>and</strong> how much money comes back<br />
out at the end <strong>of</strong> the day, perhaps by arranging through some trick<br />
to get access to the owner’s briefcase in the morning <strong>and</strong> evening. If<br />
the amount <strong>of</strong> money that comes out every day is greater than the<br />
amount that went in, <strong>and</strong> if they’re convinced there is no safe on the<br />
premises holding a large reservoir <strong>of</strong> money, then the owner must<br />
be counterfeiting. This inflow-equals-outflow technique is useful if<br />
we are sure that there is a region <strong>of</strong> space within which there is no<br />
supply <strong>of</strong> mass that is being built up or depleted.<br />
A stream <strong>of</strong> water example 1<br />
If you watch water flowing out <strong>of</strong> the end <strong>of</strong> a hose, you’ll see<br />
that the stream <strong>of</strong> water is fatter near the mouth <strong>of</strong> the hose, <strong>and</strong><br />
skinnier lower down. This is because the water speeds up as it<br />
falls. If the cross-sectional area <strong>of</strong> the stream was equal all along<br />
its length, then the rate <strong>of</strong> flow (kilograms per second) through a<br />
lower cross-section would be greater than the rate <strong>of</strong> flow through<br />
a cross-section higher up. Since the flow is steady, the amount<br />
<strong>of</strong> water between the two cross-sections stays constant. <strong>Conservation</strong><br />
<strong>of</strong> mass therefore requires that the cross-sectional area <strong>of</strong><br />
the stream shrink in inverse proportion to the increasing speed <strong>of</strong><br />
the falling water.<br />
self-check A<br />
Suppose the you point the hose straight up, so that the water is rising<br />
rather than falling. What happens as the velocity gets smaller? What<br />
happens when the velocity becomes zero? ⊲ Answer, p. 909<br />
How can we apply a conservation law, such as conservation <strong>of</strong><br />
mass, in a situation where mass might be stored up somewhere? To<br />
use a crime analogy again, a prison could contain a certain number<br />
<strong>of</strong> prisoners, who are not allowed to flow in or out at will. In physics,<br />
this is known as a closed system. A guard might notice that a certain<br />
prisoner’s cell is empty, but that doesn’t mean he’s escaped. He<br />
could be sick in the infirmary, or hard at work in the shop earning<br />
cigarette money. What prisons actually do is to count all their<br />
prisoners every day, <strong>and</strong> make sure today’s total is the same as