Physics I
Class 09
Conservation of Momentum
in One Dimension
09-1
What is a System of Objects?
The universe is too large. To learn physics,
we need to concentrate our attention on just
a small part of it. If we do things right, we
can select a small group of interacting
objects in such a way that the phenomenon
we want to study is not significantly
influenced by anything else.
How to “do things right” is the tricky part.
A “system of objects” is a subset of the universe
that we have selected to study a phenomenon.
09-2
Internal and External Forces
Our system here consists of Objects A and B.
Forces between A and B are internal forces.
Forces on A or B from sources outside the system are external forces.
If we change the definition of the system, could that affect which forces
are internal and which are external?
F on A from C
F on B from C
External Forces
F on A from B F on B from A
Object A
Internal Forces
Object B
09-3
The Momentum of a System
The momentum of a system is the sum of all the individual parts:
 N 
P   pi
i 1
Newton’s Second Law for each object:


 d pi
Fnet ,i  m a i 
dt
Newton’s Second Law for the system:
 N 

dP
d pi N 

  Fnet ,i   F
d t i 1 d t i 1
all system
09-4
Cancellation of Internal Forces
Some forces in a system are internal, some are external.



 F   Fint   Fext
all system
The internal forces are all in Newton’s Third Law Pairs
within the system, so they sum exactly to zero in the system.



 F  0   Fext  Fext
all system
09-5
Conservation of Momentum
(in a Nutshell)
Only external forces can change the momentum of a system.


dP
  Fext
dt

If the external forces cancel and/or can be neglected, thenP is
constant (zero time derivative), or as physicists say, conserved.

dP
0
dt
09-6
One-Dimensional Example
Two Carts on a Track
Two objects are initially at rest, P = 0.
The objects spring apart; the spring force is internal to the system.
After the spring pushes them apart, because P is conserved:
p1
p2
Pafter  Pbefore
P  p1  p 2  0  m1v1  m 2 v 2
m1v1   m 2 v 2
09-7
Class #9
Take-Away Concepts
1.
2.
Systems; internal/external forces in systems.
Momentum defined for a system:
 N 
P   pi
i 1
3.
Newton’s
 Second Law for a system:

dP
  Fext
dt
4. Conservation
of momentum when


dP
  Fext  0
dt
Pafter  Pbefore
09-8
Activity #9 Conservation of Momentum
Objectives of the Activity:
1.
2.
Think about how systems are defined and how that
affects the classification of internal/external forces.
Use VideoPoint to study conservation of momentum for
a two-object system in one dimension.
09-9