1. Momentum and Its Conservation
Chapter 9
Momentum and Its Conservation

2. Momentum is the product of an object’s mass and velocity.
Formula for momentum
Momentum is the product of an object’s mass and velocity.
p=mv

3. Why p?
Momentum is so fundamental in Newtonian mechanics that Newton called it a “quantity of motion”
Mathematician Gottfried Leibniz used the term progress to mean “quantity of motion with which a body proceeds in a certain direction”.

4. Law of Conservation of Momentum
The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.

5. Basic Momentum Problems Directions: Solve for the momentum problems below. Make sure to put these in your NOTEBOOK!
A. 75 kg speed skater moving forward at 16 m/s
B kg ostrich running north at 16.2 m/s
C kg baby on a train moving eastward at 72 m/s
D kg kitten running to the left at 6.5 m/s
E kg passenger on a train stopped on the tracks

6. Law of Conservation of Momentum
Total Initial Momentum = Total Final Momentum

7. COLLISIONS

9. Types of Collisions Elastic vs. Inelastic
Elastic Collision- Two objects collide and move separately after the collision.
The total momentum and the total kinetic energy is conserved

10. Inelastic Collision
A collision in which two objects stick together after colliding.
Momentum is conserved
The final velocity is the same for both objects since they are stuck together

11. You need to be able to:
Apply conservation of momentum to solve simple collision problems. (P3.5a)

12. What type of collision?

13. Find the velocity of the ice skater
Law of Conservation of energy states that momentum before collision=momentum after the collision
Before p=(12 kg)(20 km/h)=240
After p= (75kg)v
V=3.2 km/h

14. Which type of collision? What is the final velocity?

15. Which type of collision? What is the final velocity?

16. Assignment: PAPER WAD
1. Write a momentum collision story problem similar to the examples given in class on a lined piece of paper. DO NOT SOLVE.
2. Crumple up paper wad. Throw it to classmate!
3. Solve the problem.
4. Crumple up paper wad. Throw it to classmate!
5. Check answer. Write a momentum story problem.
6. Crumple up paper wad. Throw it to classmate!
7. Solve the problem.
8. Crumple up paper wad. Throw it to classmate!
9. Check answer……

17. Impulse and Momentum 9.1 Impulse and Momentum
Section
Impulse and Momentum
9.1
Impulse and Momentum
Impulse- the product of the average force on an object and the time interval over which it acts.
Impulse= FΔt Units are N*s

18. Impulse and Momentum 9.1 Impulse and Momentum
Section
Impulse and Momentum
9.1
Impulse and Momentum
Recall the equation (2nd Law) F=ma, then F=m(Δv/t).
It can be rearranged so that FΔt = mΔv
The right side of this equation, pf − pi, describes the change in momentum of an object. Thus, the impulse on an object is equal to the change in its momentum, which is called the impulse-momentum theorem.
FΔt = pf − pi

19. Impulse and Momentum 9.1 Using the Impulse-Momentum Theorem
Section
Impulse and Momentum
9.1
Using the Impulse-Momentum Theorem
Impulse is the area under a curve on force-time graphs. In this graph the impulse =13.1 N·s
Because 1 N·s is equal to 1 kg·m/s, the momentum gained by the ball is kg·m/s in the direction of the force acting on it.

20. Section
Impulse and Momentum
9.1
Using the Impulse-Momentum Theorem to Save Lives
Air bags- exert force on larger area of a person’s body, reducing the force during collision. Also, air bags increase the time interval .
The cushions in athletic shoes are designed to reduce the force of impact by increasing the time interval of when the force is applied to the ground.

21. Conservation of Momentum
Section
Conservation of Momentum
9.2
Momentum is conserved in a Closed, Isolated System
Under these conditions, the law of conservation of momentum states that the momentum of any closed, isolated system does not change
The first and most obvious condition is that no balls are lost and no balls are gained. Such a system, which does not gain or lose mass, is said to be a closed system.
When the net external force on a closed system is zero, the system is described as an isolated system.