Conservation of Momentum Quantitative Examples
Example 1
A man of mass 70. kg and a boy of mass 35 kg are standing together on a
smooth ice surface. They push each other apart so that the man moves away
with a speed of 0.30 m . What is the final velocity of the boy?
s
If the system includes both the man and the boy it is then an isolated, closed system and
momentum is conserved.
Momentum Conservation Equation:
 
pi  p f


0  pmf  pbf
Conservation of Momentum Quantitative Examples
Example 1
A man of mass 70. kg and a boy of mass 35 kg are standing together on a
smooth ice surface. They push each other apart so that the man moves away
with a speed of 0.30 m . What is the final velocity of the boy?
s
Momentum Conservation Equation:
 
pi  p f


0  pmf  pbf


pbf   pmf


mbvbf  mmvmf
mm 

vbf  
vmf
mb

70. kg

vbf  
 0.30 m
s
35 kg

vbf  0.60 m
s

Notice the boy
has half the
mass so twice
the velocity!
Example 2
Conservation of Momentum Quantitative Examples
A bullet of mass 10. g moves horizontally with a speed of 400. m and embeds
s
itself in a block of wood of mass 0.39 kg that is initially at rest on a frictionless table
as shown below.
a. What is the final velocity of the bullet and the block after the collision?
If the system includes both the bullet and the wood it is then an isolated, closed system
and momentum is conserved.
Momentum Conservation Equation:
 
pi  p f


pBi  p f


mbvbi  mb  mw v f
Example 2
Conservation of Momentum Quantitative Examples
A bullet of mass 10. g moves horizontally with a speed of 400. m and embeds
s
itself in a block of wood of mass 0.39 kg that is initially at rest on a frictionless table
as shown below.
a. What is the final velocity of the bullet and the block after the collision?
Momentum Conservation Equation:
 
pi  p f


pBi  p f




mbvbi  mb  mw v f

vf 
mb 
vbi
mb  mw

vf 
0.010 kg
400. m
s
0.010 kg  0.39 kg

v f  10. m

s
