1. Chapter 7
Impulse and Momentum

2. Momentum is a product of the mass of an object and its velocity.
7.1 Momentum Theorem
Momentum is a product of the mass of an object and its velocity.
Mathematically, momentum is given by:
p = mv
m represents mass in kg
v represents velocity in m/s
p represents momentum in kg m/s
Momentum is a vector quantity whose direction is that of the velocity.

3. 7.1 Momentum Theorem
Problem 1
Find the momentum of an auto with mass 1350 kg traveling 75 km/h.
Problem 2
Find the velocity that a bullet of mass 1.0 X 10-2 kg would have to have so that it has the same momentum as a lighter bullet of mass 1.8 X 10-3 kg and velocity 325 m/s.
Problem 3
A 16 gram mass is moving in the positive x direction at 0.3 m/s while a 4 gram mass is moving in the negative x-direction at 0.5 m/s.
What is the momentum of the 16 gram mass?
What is the momentum of the 4 gram mass?

4. 7.1 The Impulse-Momentum Theorem
There are many situations when the
force on an object is not constant.

5. 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 can also be described as a change in momentum.
Impulse is a vector quantity and has the same direction
as the average force.

6. 7.1 The Impulse-Momentum Theorem

7. 7.1 The Impulse-Momentum Theorem
Problem 4
A 2 kg brick is moving at a speed of 6 m/s. How large a force is needed to stop the brick in a time of 7 X 10-4 seconds?
Problem 5
A kg ball moving in the positive x direction at 13 m/s is hit by a bat. Its final velocity is 19 m/s in the negative x direction. The bat acts on the ball for 0.01 s. Find the average force exerted on the ball by the bat.
Problem 6
Page 191 of Textbook, Question 2.
Problem 7
Page 191 of Textbook, Question 5

8. 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.

9. 7.1 The Impulse-Momentum Theorem

10. 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

11. 7.1 The Impulse-Momentum Theorem
Example 2 A Rain Storm
Rain comes down with a velocity of -15 m/s and hits the
roof of a car. The mass of rain per second that strikes
the roof of the car is kg/s. Assuming that rain comes
to rest upon striking the car, find the average force
exerted by the rain on the roof.

12. 7.1 The Impulse-Momentum Theorem
Neglecting the weight of
the raindrops, the net force
on a raindrop is simply the
force on the raindrop due to
the roof.

13. 7.2 The Principle of Conservation of Linear Momentum
WORK-ENERGY THEOREM CONSERVATION OF ENERGY
IMPULSE-MOMENTUM THEOREM ???
Apply the impulse-momentum theorem to the midair collision
between two objects…..

14. 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.

15. 7.2 The Principle of Conservation of Linear Momentum
The internal forces cancel out.

16. 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.

17. 7.2 The Principle of Conservation of Linear Momentum
Example 6 Ice Skaters
Starting from rest, two skaters
push off against each other on
ice where friction is negligible.
One is a 54-kg woman and
one is a 88-kg man. The woman
moves away with a speed of
+2.5 m/s. Find the recoil velocity
of the man.

18. 7.2 The Principle of Conservation of Linear Momentum

19. 7.2 The Principle of Conservation of Linear Momentum
Applying the Principle of Conservation of Linear Momentum
1. Decide which objects are included in the system.
2. Relative to the system, identify the internal and external forces.
3. Verify that the system is isolated.
4. Set the final momentum of the system equal to its initial momentum.
Remember that momentum is a vector.

20. 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/perfectly inelastic.

21. 7.3 Collisions in One Dimension
Example 8 A Ballistic Pendulim
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.

22. 7.3 Collisions in One Dimension
Apply conservation of momentum
to the collision:

23. 7.3 Collisions in One Dimension
Applying conservation of energy
to the swinging motion:

24. 7.3 Collisions in One Dimension

25. 7.1 The Impulse-Momentum Theorem
Problem 8
A 98 kg parts cart with rubber bumpers rolling 1.2 m/s to the right crashes into a similar cart of mass 125 kg moving left at 0.75 m/s. After the collision, the lighter cart is traveling m/s to the left. What is the velocity of the heavier cart after the collision?
Problem 9
One cart of mass 15 kg is moving 5 m/s to the right on a frictionless track and collides with a cart of mass 3 kg. The final velocity of the carts that become stuck together after the collision is 1.5 m to the right. Find the velocity of the second cart before the collision.
Problem 10
A X 104 kg railroad car traveling 8 m/s to the east collides and couples with a stopped 2.25 X 104 kg railroad car. What is the velocity of the joined railroad cars after the collision?

26. 7.4 Collisions in Two Dimensions
A Collision in Two Dimensions

27. 7.4 Collisions in Two Dimensions

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

29. 7.5 Center of Mass

30. In an isolated system, the total linear momentum does not change,
7.5 Center of Mass
In an isolated system, the total linear momentum does not change,
therefore the velocity of the center of mass does not change.

31. 7.5 Center of Mass
BEFORE
AFTER

32. Practice Problems Question 1
A railroad car of mass 2.25 X 104 kg is traveling east at 5.5 m/s and collides with a railroad car of mass 3.0 X 104 kg traveling west at 1.5 m/s. Find the velocity of the railroad cars that become coupled after the collision.
Question 2
A 4-g bullet is fired from a 4.5 kg gun with a muzzle velocity of 625 m/s. What is the speed of recoil of the gun?