1. MOMENTUM

2. Momentum
Momentum is defined as the product of a body’s mass and its velocity
The Equation: p=mv p= momentum
m= mass
v= velocity
The units for momentum are kg*m/s

3. Momentum From the equation you can see the following
As mass increases, momentum increases
As velocity increases, momentum increases
A small object with great velocity can have as much damaging momentum as a large object moving slowly. (a bullet vs a slowing moving truck)
An objects momentum will always be in the same direction as the objects velocity
Since velocity is a vector quantity, so is momentum

4. Sample Problem
An object of mass 14kg travels a distance of 26m for 12 sec. How much momentum does the object have?

5. II. Impulse and Momentum
Since momentum is dependent on an objects velocity, we know the momentum will change if the velocity changes.
Any change in velocity will come only if the object is accelerated or decelerated. This means we will apply a force to the object.
Hence, we can say that force causes a change in an objects momentum.
If we apply a force over a given time to change an objects momentum, it is called an impulse.

6. Mathematically: J= F* t J= impulse p=F*t F=force t = time
The units for impulse are N*s or kg*m/s
Impulse is a vector quantity

7. Sample Problem:
An object is moving eastward. A force of 10 N east is applied for 6 sec.
What impulse has been applied?
What will happen to the objects momentum?

8. IMPULSE:
Since an impulse can cause momentum, or change momentum we can safely say “Impulse= change in momentum” Or
J=p
Or (mathematically)
F*t=mv

9. Equation
This equation allow us to see the effect the variables of force + velocity have on momentum and impulse.
This equation actually tells us 3 things:
An unbalanced force acting on an object will cause a momentum change.
The direction of the momentum will be the same as the applied force
The magnitude (amount) of the change will be proportional to the force and the length of time the force acts.

10. Sample Problem
A power boat weighs 4550N. It reaches a speed of 45m/s because of an applied force of 800N East.
What is the boat’s mass?
How long did the force act?
In what direction is the object’s momentum?

11. III. Conservation of Momentum
In nature, certain substances are said to be conserved.
When we say a substance is conserved, we mean it is not created or destroyed, it just changes form.
Examples of conserved substances in nature include matter, energy, impulse, and momentum
This means that momentum cannot be created or destroyed, nor is it “lost” during a collision. It just changes form.

12. Example:
As an example, think of two trucks moving at each other. They move at the same speed, collide head on, then stop. What happened to their momentum’s?
Since both trucks stopped we think they ‘lost’ their momentum. Technically, it’s not lost, it has just been transferred to the ground. Hence, momentum has been conserved.

13. Momentum before = Momentum after
Equation:
We can write the law of conservation of momentum in equation form, it reads:
Momentum before = Momentum after or
p before = pafter
mv before = mv after
We will derive equations from the above depending on the given information. Here are samples of the most common situations, with sample equations.

14. Examples
Situation 1:One object is at rest. A second object is pushed into it. After the collision, one object moves one way, the other the opposite way.
What is your momentum equation?
Situation 2: A bullet and gun are both at rest. The gun is fired, the bullet travels out of the barrel as the gun recoils.

15. More examples
Situation 3: Two objects move towards each other. They collide, stay together, then move off in the same direction.
What is your momentum equation?
Situation 4: Two objects move in the same direction, they collide, then move off in the same direction (separately)

16. Situation 4 cont.
before 1 2
m1v1 + m2v2
after 1 2
m1v1l + m2v21 =
Situation 4 is the most common of the collision problems. In fact, the equation you derived for 4 is known as ‘the general form of the conservation of momentum equation”

17. General Form of Conservation of Momentum Equation
m1 = mass of 1st object
m2 = mass of 2nd object
v1 = velocity of 1st object
v2 = velocity of 2nd object
v11 = new velocity of 1st object.
v21 = new velocity of 2nd object
m1v1 + m2v2 = m1v11 + m2v21

18. About the equation:
Note that mass is not affected by the collision, only the velocity.
Also notice (please!) that the other 3 equations you derived are just variations of this general one.
Given a different situation, you need to derive your own equation
Always remember: “Total momentum at beginning = total momentum at end”

19. Sample Problems: Derive your own momentum equation, then solve:
A bullet of mass .25kg sits in a 10kg gun. What is the momentum of the system after the gun is fired?
A car of mass 5000kg sits in a parking space. It is hit by a 6000kg car moving at 5m/s. Both cars move forward together. What speed are they moving at?

20. Sample Problem:
3. Two tractor trailers, each of mass 15,000kg are moving east down the thruway. One is moving at 20m/s, the other at 15m/s. They collide, then continue moving east. The truck moving at 15m/s now moves at 16.2m/s. What speed is the other truck moving at?

21. Elastic Collisions
In the real world we know of two types of collisions, elastic and inelastic.
Elastic collisions are also know as perfect collisions. They rarely happen here, unless the objects are very massive, or moving very fast.
Two tractor trailers, or two bullets have close to elastic collisions, meaning little momentum is transferred to the ground or atmosphere

22. Inelastic collisions
Inelastic collisions are also known as “imperfect” collisions. Momentum is transferred to the ground or atmosphere.
In a world full of friction, inelastic collisions are the rule.