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Chapter 3 Energy and Conservation Laws

Chapter 3 Energy and Conservation Laws. 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.

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Chapter 3 Energy and Conservation Laws

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  1. Chapter 3Energy 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 2nd 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. ExampleExample 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. ExampleExample 3.1 ANSWER: The problem gives us: The force is:

  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. • doubles. • quadruples. • 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 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. ExampleExample 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. ExampleExample 3.2 ANSWER: The problem gives us: The momentum before: The momentum after:

  23. ExampleExample 3.2 ANSWER: Conserving momentum

  24. ExampleExample 3.2 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.

  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 thegas because it has more mass

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