1. Chapter 7
Impulse and Momentum

2. 7.1 The Impulse-Momentum Theorem
There are many situations when the
force on an object is not constant.

3. 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:
Impulse is a vector quantity and has the same direction
as the average force.

4. 7.1 The Impulse-Momentum Theorem

5. 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:
Linear momentum is a vector quantity and has the same
direction as the velocity.

6. 7.1 The 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
final momentum
initial momentum

7. 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.

8. 7.2 The 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.

9. 7.2 The 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.

10. 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.

11. 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 kg. The block
swings to a maximum height of
0.650 m above the initial position.
Find the initial speed of the
bullet.

12. 7.3 Collisions in One Dimension
Apply conservation of momentum
to the collision:

13. 7.3 Collisions in One Dimension
Applying conservation of energy
to the swinging motion:

14. 7.3 Collisions in One Dimension

15. 7.4 Collisions in Two Dimensions

16. The center of mass is a point that represents the average location for
the total mass of a system.

17. 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

18. 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

19. 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

20. B7. 4 A billiard ball moving at 10
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 ; º