Physics 102: Chapter 6 - Momentum

1. Physics 102: Chapter 6 - Momentum Momentum and Energy views of force Impulse-Momentum Theorem What does conservation mean Conservation of Momentum

2. Exam 2 - On Wednesday Exam notes Must be handwritten on 8.5” x 11” piece of paper Cannot be torn out of a notebook No worked out examples, derivations, or solutions Corrections and Notes from Exam 1 available in your boxes > Noon tomorrow Review Session tomorrow night from 7-9 PM in RH 114

3. Whenever an interaction occurs in a system, forces occur in equal and opposite pairs. Which of the following do not always occur in equal and opposite pairs? 1. Impulses.2. Accelerations.3. Momentum changes.4. All of these occur in equal and opposite pairs.5. None of these do.

4. 2. Accelerations. Whenever an interaction occurs in a system, forces occur in equal and opposite pairs. Which of the following do not always occur in equal and opposite pairs? Because the time interval for each interaction part is the same, impulses and momentum changes also occur in equal and opposite pairs. But not necessarily accelerations, because the masses of the interaction may differ. Consider equal and opposite forces acting on masses of different magnitude.

5. Which would be more damaging? 1. Driving into a massive concrete wall.2. Driving at the same speed into a head- on collision with an identical car traveling toward you at the same speed.3. They are equivalent.

6. Which would be more damaging? 3. They are equivalent. Your car decelerates to a dead stop either way. The dead stop is easy to see when hitting the wall, and a little thought will show the same is true when hitting the car. If the oncoming car were traveling more slowly, with less momentum, you’d keep going after the collision with more “give,” and less damage (to you). But if the oncoming car had more momentum than you, it would keep going and you’d snap into a sudden reverse with greater damage. Identical cars at equal speeds means equal momenta—zero before, zero after collision.

7. Reading Quiz • Impulse is • a force that is applied at a random time. • a force that is applied very suddenly. • the area under the force curve in a force-versus-time graph. • the interval of time that a force lasts. Slide 9-2

8. Answer • Impulse is • the area under the force curve in a force-versus-time graph. Slide 9-3

9. Reading Quiz • 2. The total momentum of a system is conserved • always. • if no external forces act on the system. • if no internal forces act on the system. • never; momentum is only approximately conserved. Slide 9-4

10. Answer • 2. The total momentum of a system is conserved • if no external forces act on the system. Slide 9-5

11. Momentum - Key Equations • 2. The total momentum of a system is conserved • if no external forces act on the system. Slide 9-5

12. Impulse Effects of Time and Force Large time => small force Small time => Large force

13. Impulse Effects of Time and Force • Pulling your hand back while you catch a ball • Bending your knees and rolling when you fall in Self defense class / Sky-Diving • Falling on a wooden floor is safer than falling on a cement floor • Railroad car couplings are loose => slow to accelerate or stop • Movies (Nail on head / hammer on hand/Inertia Balls)(Table top pull movie)Table top friction pull

14. Shut the Door You are sittingon your bed in your dorm room, and suddenly you hear the voice of your ex coming down the hall. You really want to avoid any contact (you broke things off a week ago), and so you want to shut the door. But you don't have time to get up and shut it and act like it wasn't on purpose. You need something fast. Sitting beside you, you happen to have a super ball and a ball of clay that you fidget with when you're studying on your bed. What do you do? • Throw the clay ball • Throw the superball • Throw either ball, it doesn’t matter Explain your answer and show why you chose one and not the other.. (Demonstration movie =>http://groups.physics.umn.edu/demo/collisionframe.html)

15. Pelton Wheel Enriching yourself with Physics During the California Gold Rush, Lester Pelton designed a water wheel that caused the water to make a U-turn, i.e. causing the water to bounce off the paddle. He made a lot of money on this invention, more than the miners.

16. Bouncing off the Wall In the overhead view shown below, a 290 g ball with a speed v of 4.6 m/s strikes a wall at an angle of 30° and then rebounds with the same speed and angle. It is in contact with the wall for 11 ms. Overhead View • What is the impulse on the ball from the wall? • What is the average force (magnitude & direction) on the wall from the ball?

17. Examples of Collisions and Explosions Oil and Water example What does conserved mean?

18. The Law of Conservation of Momentum In terms of the initial and final total momenta:   Pf = Pi In terms of components: Slide 9-18

19. Perfectly Inelastic Collision Example

20. Defining your system - system schema Isolated system is when the sum of all external forces is zero.

21. Slide 9-19

22. Example A curling stone, with a mass of 20.0 kg, slides across the ice at 1.50 m/s. It collides head on with a stationary 0.160-kg hockey puck. After the collision, the puck’s speed is 2.50 m/s. What is the stone’s final velocity? Slide 9-20

23. Inelastic Collisions For now, we’ll consider perfectly inelastic collisions: A perfectly elastic collision results whenever the two objects move off at a common final velocity. Slide 9-21

24. Jack and the Skateboard -- Example 1 Jack stands at rest on a skateboard. The mass of Jack and the skateboard together is 75 kg. Ryan throws a 3.0 kg ball horizontally to the right at 4.0 m/s to Jack, who catches it. What is the final speed of Jack and the skateboard? Slide 9-22

25. Bullet and Block -- Example 2 A 10 g bullet is fired into a 1.0 kg wood block, where it lodges. Subsequently, the block slides 4.0 m across a floor (µk = 0.20 for wood on wood). What was the bullet’s speed? Slide 9-23

26. Professor on Ice -- Explosion Example A professor of physics is going ice skating for the first time. He has gotten himself into the middle of an ice rink and cannot figure out how to make the skates work. Every motion he makes simply slips on the ice and leaves him in the same place he started. He decides that he can get off the ice by throwing his gloves in the opposite direction. Suppose he has a mass M and his gloves have a mass m. If he throws them as hard as he can away from him, and they leave his hand with a velocity v. Explain whether or not he will move. If he does move, calculate his velocity, V. Discuss his motion from the point of view of the forces acting on him. If the ice rink is 10 m in diameter and the skater starts in the center, estimate how long it will take him to reach the edge, assuming there is no friction at all Slide 9-5

27. Reading Quiz • In an inelastic collision, • impulse is conserved. • momentum is conserved. • force is conserved. • mechanical energy is conserved. • elasticity is conserved. Slide 9-6

28. Answer • In an inelastic collision, • momentum is conserved. Slide 9-7