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Momentum is conserved in any collision if the effect of any external
forces present is
negliable relative to the effect of the collision. Consider a collision as
shown in Figure (6.1).
Figure 6.1:
1D Collision

Apply the impulsemomentum theorem to m_{1} and m_{2} separately,
t

=

p_{1} = m_{1}v_{1f}  m_{1}v_{1i}
 
t

=

p_{2} = m_{2}v_{2f}  m_{2}v_{2i}
 
where = the average force of m_{2} on m_{1} , and = the
average force of m_{1} on m_{2} . By Newton's third law
F_{1}(t) =  F_{2}(t)
which gives
=  and so,
( + )t = m_{1}v_{1f}  m_{1}v_{1i} + m_{2}v_{2f}  m_{2}v_{2i} = 0


 
p_{1f} + p_{2f} = p_{1i} + p_{2i}.


 (4) 
This is the statement of the conservation of momentum.
Note:
 The system must be isolated: the affect of all external forces acting on
m_{1} and m_{2} must be negligable.
 The conservation of momentum holds for a collision involving any number
of objects:
 Momentum is a vector, and each component is conserved separately.
The equation for conservation of momentum really contains three equations,
one for each dimension.
Next: Collisions and Kinetic Energy
Up: Momentum and Collisions
Previous: Momentum and Impulse
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10/9/1997