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Chapter 7
Impulse and Momentum
7.1 The Impulse-Momentum Theorem
There are many situations when the
force on an object is not constant.
7.1 The Impulse-Momentum Theorem
DEFINITION OF IMPULSE
The impulse of a force is the product of the average
force and the time interval during which the force acts:
 
J  F t
Impulse is a vector quantity and has the same direction
as the average force.
newton  seconds (N  s)
7.1 The Impulse-Momentum Theorem
 
J  F t
7.1 The Impulse-Momentum Theorem
DEFINITION OF LINEAR MOMENTUM
The linear momentum of an object is the product
of the object’s mass times its velocity:


p  mv
Linear momentum is a vector quantity and has the same
direction as the velocity.
kilogram  meter/seco nd (kg  m/s)
7.1 The Impulse-Momentum Theorem
IMPULSE-MOMENTUM THEOREM
When a net force acts on an object, the impulse of
this force is equal to the change in the momentum
of the object
impulse
 



 F t  mvf  mvo
final momentum
initial momentum
7.2 The Principle of Conservation of Linear Momentum
Internal forces – Forces that objects within
the system exert on each other.
External forces – Forces exerted on objects
by agents external to the system.
7.2 The Principle of Conservation of Linear Momentum
PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM
The total linear momentum of an isolated system is constant
(conserved). An isolated system is one for which the sum of
the average external forces acting on the system is zero.
7.2 The Principle of Conservation of Linear Momentum
PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM
The total linear momentum of an isolated system is constant
(conserved). An isolated system is one for which the sum of
the average external forces acting on the system is zero.
In the top picture the net external force on the
system is zero.
In the bottom picture the net external force on the
system is not zero.
7.3 Collisions in One Dimension
The total linear momentum is conserved when two objects
collide, provided they constitute an isolated system.
Elastic collision -- One in which the total kinetic
energy of the system after the collision is equal to
the total kinetic energy before the collision.
Inelastic collision -- One in which the total kinetic
energy of the system after the collision is not equal
to the total kinetic energy before the collision; if the
objects stick together after colliding, the collision is
said to be completely inelastic.
7.3 Collisions in One Dimension
Example 8 A Ballistic Pendulum
The mass of the block of wood
is 2.50-kg and the mass of the
bullet is 0.0100-kg. The block
swings to a maximum height of
0.650 m above the initial position.
Find the initial speed of the
bullet.
7.3 Collisions in One Dimension
Apply conservation of momentum
to the collision:
m1v f 1  m2 v f 2  m1vo1  m2 vo 2
m1  m2 v f
vo1 
 m1vo1
m1  m2 v f
m1
7.3 Collisions in One Dimension
Applying conservation of energy
to the swinging motion:
mgh  12 mv 2
m1  m2 ghf
 12 m1  m2 v 2f
gh f  12 v 2f


v f  2 gh f  2 9.80 m s 2 0.650 m
7.3 Collisions in One Dimension


v f  2 9.80 m s 2 0.650 m
vo1 
m1  m2 v f
m1
 0.0100 kg  2.50 kg 
 29.80 m s 2 0.650 m   896 m s
vo1  
0.0100 kg


7.4 Collisions in Two Dimensions
m1v f 1x  m2 v f 2 x  m1vo1x  m2 vo 2 x
m1v f 1 y  m2 v f 2 y  m1vo1 y  m2 vo 2 y
7.5 Center of Mass
The center of mass is a point that represents the average location for
the total mass of a system.
xcm
m1 x1  m2 x2

m1  m2
Problems to be solved
• 7.8, 7.34, 7.41, 7.44, 7.60, 7.64
• B7.1 A 1000kg car moving at 20m/s hits a
2000kg parked car head on. How much
mechanical energy is dissipated if the
collision is (a) elastic, (b) completely
inelastic? Ans.: (a)None, because
mechanical energy is conserved during
elastic collisions. (b) 13.33×104J
• B7.2 A bullet of mass 10-2kg and initial
horizontal velocity of 250m/s strikes and is
embedded in a 1kg wooden block. The
wooden block hangs on the end of a long
string. (a) What is the velocity of the block
and bullet after impact? (b) How high will
the block and bullet swing upward? Ans:
(a) 2.48m/s (b) 0.31m
• B7.3 Two cars approaching each other
along streets that meet at a right angle
collide at the intersection. After the crash,
they stick together. If one car has a mass
of 1450kg and an initial speed of 11.5m/s
and the other has a mass of 1750kg and
an initial speed of 15.5m/s, what will be
their speed and direction immediately after
impact? Ans: 9.95m/s ; 58.4º
• B7.4 A billiard ball moving at 10.0m/s
along the positive x-axis collides with a
second billiard ball at rest. The balls have
identical masses. After the collision, the
incoming (or incident) ball moves on with a
speed of 7.7m/s at an angle of 40⁰ from
the x-axis. What are the speed and
direction of motion of the struck ball?
Ans: 6.43m/s ; -50.37º