7.2 Conservation of Linear Momentum
We talked last time how Newton’s Laws naturally show up in our discussions of
momentum.
It turns out we can write all of Newton’s Laws in terms of momentum:
1.
Law of Inertia
:
A body at rest will remain at rest, and a body in motion will
continue in straight line motion unless acted upon by some external force.
constant
=
p
v
a
m
F
v
v
=
p
Δ
=
⇒
v
v
2.
t
F
Δ
Force equals the rate of change of momentum.
3.
Action Equals Reaction:
21
12
F
F

=
t
p
t
p
Δ
Δ

=
Δ
Δ
⇒
2
1
2
1
p
p
Δ

=
Δ
⇒
*Changes in the momentum are of equal magnitude and in opposite directions!
What are the consequences of this???
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Let’s just consider the simplest interacting system that we can.
Such a system
will consist of two particles,
m
1
and
m
2
, interacting with each other.
m
1
m
2
Assume for now that the two particles form an isolated system from the rest of the
universe, and the only forces they experience are their mutual forces.
In other words, there are no external forces.
Let the net force on particle 1 by 2 be
F
.
F
Then by Newton’s 3
rd
Law, we know that the
net force on particle 2 is
–F
.
F
By Newton’s 2
nd
Law.
t
p
F
Δ
Δ
=
1
t
p
F
Δ
Δ
=

2
Now let’s add these two equations together.
t
p
t
p
F
F
Δ
Δ
+
Δ
Δ
=

+
2
1
)
(
0
=
0
)
(
2
1
=
Δ
+
Δ
⇒
t
p
p
,
0
=
Δ
Δ
⇒
t
P
where
, the total momentum
.
2
1
p
p
P
+
=
Thus,
does not change in time.
In other words, it is a constant of the
motion
!
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 Fall '08
 SPRUNGER
 Physics, Inertia, Momentum, Law of Conservation of Momentum, total momentum, PF

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