1. Vern J. Ostdiek Donald J. Bord Chapter 3 Energy and Conservation Laws

2. Conservation laws The most fundamental ideas we have in physics are conservation laws. Statements telling us that some quantity does not change Conservation of mass states: The total mass of an isolated system is constant. To apply these, we must define a “system.”

3. Conservation laws, cont’d A system is just a collection of objects we decide to treat at one time. The tanker and fighter can represent a system. The fuel leaving the tanker goes into the fighter: mass is conserved

4. Linear momentum Linear momentum is defined as the product of an object’s mass and its velocity. We typically just say momentum.

5. Linear momentum, cont’d Momentum is a measure of an object’s state of motion. Consider an object whose momentum is 1 kg·m/s This could be a 0.005 kg bullet traveling at 200 m/s. This could be a 0.06 kg tennis ball traveling at 16.7 m/s.

6. Linear momentum, cont’d Momentum (continued) high mass or high velocity  high momentum high mass and high velocity  higher momentum low mass or low velocity  low momentum low mass and low velocity  lower momentum

7. Linear momentum, cont’d Newton’s 2 nd law is closely related to momentum. The net external force acting on an object equals the rate of change of linear momentum:

8. Linear momentum, cont’d How is this related to F = ma?

9. Example Example 3.1 Let’s estimate the average force on a tennis ball as it is served. The ball’s mass is 0.06 kg and it leaves the racquet with a speed of 40 m/s. High-speed photography indicates that the contact time is about 5 milliseconds.

10. ANSWER: The problem gives us: The force is: Example Example 3.1

11. Linear momentum, cont’d This tells why we must exert a force to stop an object or get it to move. To stop a moving object, we have to bring its momentum to zero. To start moving an object, we have to impart some momentum to it.

12. Momentum When the speed of an object is doubled, its momentum: A.remains unchanged in accord with the conservation of momentum. B. doubles. C. quadruples. D. decreases.

13. Impulse The change in momentum of an object is equal to the impulse applied to it (force multiplied by the time interval during which the force is applied). Impulse = The change of momentum, or the Force multiplied by time, is called “Impulse”.

14. Impulse Impulse tells us that we can change the momentum using various forces and time intervals. You can get the same impulse by using a large force for a short time, or using a small force for a long time.

15. Impulse product of force and contact time impulse = force  time = Ft great force for long time  large impulse same force for short time  smaller impulse

16. Impulse When the force that produces an impulse acts for twice as much time, the impulse is doubled as well. Example: golfer follows through while hitting the golf ball

17. Impulse When a car is out of control, it is better to hit a haystack than a concrete wall. Common sense, but with a physics reason: Same impulse occurs either way, but extension of hitting time reduces hitting force.

18. Conservation of momentum The Law of Conservation of Momentum states: The total momentum of an isolated system is constant (no external forces). A system will have the same momentum both before and after any interaction occurs. When the momentum does not change, we say it is conserved.

19. Conservation of linear momentum, cont’d This law helps us deal with collisions. If the system’s momentum can not change, the momentum before the collision must equal that after the collision.

20. Conservation of linear momentum, cont’d We can write this as: To study a collision: Add the momenta of the objects before the collision. Add the momenta after the collision. The two sums must be equal.

21. Example Example 3.2 A 1,000 kg car (car 1) runs into the rear of a stopped car (car 2) that has a mass of 1,500 kg. Immediately after the collision, the cars are hooked together and have a speed of 4 m/s. What was the speed of car 1 just before the collision?

22. ANSWER: The problem gives us: The momentum before: The momentum after: Example Example 3.2

23. ANSWER: Conserving momentum Example Example 3.2

24. DISCUSSION: Both cars together have more mass than just car 1. Since both move away at 4 m/s, the lighter car 1 must have a greater speed before the collision. Example Example 3.2

25. Conservation of linear momentum, cont’d How do rockets work? The exhaust exits the rocket at high speed. We need high speed because the gas has little mass. The rocket moves in the opposite direction. Not as fast as the gas because it has more mass