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Chapter 26
Impulse and Momentum
180
26
Impulse and Momentum
First, a Few More Words on Work and Energy, for Comparison Purposes
Imagine a gigantic air hockey table with a whole bunch of pucks of various masses, none of
which experiences any friction with the horizontal surface of the table.
Assume air resistance to
be negligible.
Now suppose that you come up and give each puck a shove, where the kind of
shove that you give the first one is special in that the whole time you are pushing on that puck,
the force has one and the same value; and the shove that you give each of the other pucks is
similar in the following respect:
To each puck you apply the same force that you applied to the
first puck, over the same exact distance.
Since you give each of the pucks a similar shove, you
might expect the motion of the pucks (after the shove) to have something in common and indeed
we find that, while the pucks (each of which, after the shove, moves at its own constant velocity)
have speeds that differ from one another (because they have different masses), they all have the
same value of the product
m
v
2
and indeed if you put a ½ in front of that product and call it
kinetic energy
K
, the common value of
2
2
1
m
is identical to the product of the magnitude of the
force used during the shove, and the distance over which the force is applied.
This latter product
is what we have defined to be the work
W
and we recognize that we are dealing with a special
case of the work energy principle
K
W
Δ
=
, a case in which, for each of the pucks, the initial
kinetic energy is zero.
We can modify our experiment to obtain more general results, e.g. a
smaller constant force over a greater distance results in the same kinetic energy as long as the
product of the magnitude of the force and the distance over which it is applied is the same as it
was for the other pucks, but it is interesting to consider how different it would seem to us, in the
original experiment, as we move from a high-mass puck to a low mass puck.
Imagine doing that.
You push on the high-mass puck with a certain force, for a certain distance.
Now you move on
to a low-mass puck.
As you push on it from behind, with the same force that you used on the
high-mass puck, you notice that the low-mass puck speeds up much more rapidly.
You probably
find it much more difficult to maintain a steady force because it is simply more difficult to “keep
up” with the low mass puck.
And of course, it covers the specified distance in a much shorter
amount of time.
So, although you push it for the same distance, you must push the low-mass
puck for a shorter amount of time in order to make it so that both pucks have one and the same
kinetic energy.
Pondering on it you recognize that if you were to push the low-mass puck for the
same amount of
time
as you did the high-mass puck (with the same force), that the low-mass
puck would have a greater kinetic energy after the shove, because you would have to push on it

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