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or something else, and are then suddenly released and pushed by the spring or |
perhaps by a little explosion. Eurther, we shall consider motion in only one |
direction. First, let us suppose that the two obJects are exactly the same, are nice |
symmetrical objects, and then we have a little explosion between them. After the |
explosion, one of the bodies will be moving, let us say toward the right, with a |
velocity ø. Then it appears reasonable that the other body is moving toward the |
left with a velocity 0, because if the objects are alike there is no reason for right |
--- Trang 200 --- |
or left to be preferred and so the bodies would do something that is symmetrical. |
Thịs is an illustration of a kind of thinking that is very useful in many problems |
but would not be brought out if we just started with the formulas. |
The first result from our experiment is that equal objects will have equal |
speed, but now suppose that we have two objects made of diferent materials, say |
copper and aluminum, and we make the two rmasses equal. We shall now suppose |
that ïf we do the experiment with two masses that are equal, even though the |
objects are not identical, the velocities will be equal. Someone might object: |
“But you know, you could do it backwards, you did not have to swppose that. You |
could đefne equal masses to mean two masses that acquire equal velocities In |
this experiment.” We follow that suggestion and make a little explosion between |
the copper and a very large piece of aluminum, so heavy that the copper flies out |
and the aluminum hardly budges. That is too much aluminum, so we reduce the |
amount until there is just a very tỉny piece, then when we make the explosion the |
aluminum goes fying away, and the copper hardly budges. hat is not enough |
aluminum. Evidently there is some right amount in between; so we keep adjusting |
the amount until the velocities come out equal. Very well then——let us turn I§ |
around, and say that when the velocities are equal, the masses are equal. 'This |
appears to be just a defnition, and it seems remarkable that we can transform |
physical laws into mere defnitions. Nevertheless, there øre some physical laws |
Involved, and if we accept this definition of equal masses, we Immediately fñnd |
one of the laws, as follows. |
Suppose we know from the foregoing experiment that two pieces of matter, |
A and B (of copper and aluminum), have equal masses, and we compare a |
third body, say a piece of gold, with the copper in the same manner as above, |
making sure that its mass is equal to the mass of the copper. lf we now make |
the experiment between the aluminum and the gold, there is nothing in logic |
that says fhese masses must be equal; however, the ezperữnent shows that they |
actually are. So now, by experiment, we have found a new law. A statement of |
this law might be: IỶ two masses are each equal to a third mass (as determined |
by cqual velocities in this experiment), then they are equal to each other. (This |
statement does noø‡ follow at all from a similar statement used as a postulate |
regarding rmathematical quantities.) From this exarmple we can see how quickly we |
start to infer things If we are careless. It is nmoøf just a delnition to say the masses |
are equal when the velocities are equal, because to say the masses are equal is to |
imply the mathematical laws of equality, which in turn makes a prediction about |
an experiment. |
--- Trang 201 --- |
As a second example, suppose that A and Ö are found to be equal by doiïng |
the experiment with one strength of explosion, which gives a certain velocity; If |
we then use a stronger explosion, will it be true or not true that the velocities |
now obtained are equal? Again, in logic there is nothing that can decide this |
question, but experiment shows that it 7s true. So, here is another law, which |
might be stated: If two bodies have equal masses, as measured by equal velocities |
at one velocity, they will have equal masses when measured at another velocity. |
trom these examples we see that what appeared to be only a deñnition really |
involved some laws of physics. |
In the development that follows we shall assume it is true that equal masses |
have equal and opposite velocities when an explosion occurs between them. We |
shall make another assumption in the inverse case: lÝ two identical obJects, |
moving in opposite directions with equal velocities, collide and stick together by |
some kind of glue, then which way will they be moving after the collision? 'Phis |
1s again a symmetrical situation, with no preference between right and left, so |
we assume that they stand still. We shall also suppose that any bwo objects of |
cequal mass, even if the objects are made of diferent materials, which collide and |
stick together, when moving with the same velocity in opposite directions will |
come to rest after the collision. |
10-3 Momentum ¿s conserved! |
W©e can verify the above assumptions experimentally: first, that 1Ý bwo sta- |
tionary objects of equal mass are separated by an explosion they will move apart |
with the same speed, and second, if two obJects of equal mass, coming together |
with the same speed, collide and stick together they will stop. 'This we can |
do by means of a marvelous invention called an air trough,X which gets rid of |
friction, the thing which continually bothered Galileo (Fig. 10-1). He could not |
QEtS) HOLES |
Ầ fïˆ S989 |
TRÀ) Y. “Z7 |
Fig. 10-1. End view of linear alr trough. |
* HH. V. Neher and R. B. Leighton, Amer. Jour. oƒ Phụas. 31, 255 (1963). |
--- Trang 202 --- |
BUMPER SPRING TOY PISTOL CAP |
SPARK ELECTRODE |
CYLINDER PISTON BUMPER SPRING |
Fig. 10-2. Sectional view of gliders with explosive Interaction cylinder |
attachment. |
do experiments by sliding things because they do not slide freely, but, by adding |
a magic touch, we can today get rid oŸ friction. Our objects will slide without |
diffculty, on and on at a constant velocity, as advertised by Galileo. 'This is |
done by supporting the objects on air. Because air has very low Íriction, an |
object glides along with practically constant velocity when there is no applied |
force. First, we use 6wo glide blocks which have been made carefully to have |
the same weight, or mass (their weight was measured really, bu we know that |
this weight is proportional to the mass), and we place a small explosive cap in |
a closed cylinder bebween the two blocks (Fig. 10-2). We shall start the blocks |
from rest at the center point of the track and force them apart by exploding the |
cap with an electric spark. What should happen? If the speeds are equal when |
they fy apart, they should arrive at the ends of the trough at the same time. Ôn |
reaching the ends they will both bounce back with practically opposite velocity, |
and will come together and stop at the center where they started. lt is a good |
test; when it is acbually done the result is Jjust as we have described (Eig. 10-3). |
PB 4đ EỚớỚ} đe |
~-——v về -~ |
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