Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 1 Momentum and Impulse Chapter 6 Linear Momentum Momentum is defined as mass times velocity. Momentum is represented by the symbol p, and is a vector quantity. p = mv momentum = mass  velocity SI unit for momentum: kg m/s A net force is required to change an object’s momentum Momentum is directly proportional to mass and speed Something big and slow can have the same momentum as something small and fast

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Equivalent Momenta Bus: m = 9000 kg; v = 16 m /s p = 1.44 ·10 5 kg · m /s Train: m = 3.6 ·10 4 kg; v = 4 m /s p = 1.44 ·10 5 kg · m /s Car: m = 1800 kg; v = 80 m /s p = 1.44 ·10 5 kg · m /s

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Equivalent Momenta (cont.) The train, bus, and car all have different masses and speeds, but their momenta are the same in magnitude. The difficulty in bringing each vehicle to rest--in terms of a combination of the force and time required--would be the same, since they each have the same momentum.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Practice A 21.0 kg child on a 5.90 kg bike is riding with a velocity of 4.50 m/s to the north. –What is the total momentum of the child and the bike? –What is the momentum of the child? –What is the momentum of the bike? Chapter 6 Section 1 Momentum and Impulse

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 1 Momentum and Impulse Chapter 6 Linear Momentum, continued Impulse –The product of the force and the time over which the force acts on an object is called impulse. –The impulse-momentum theorem states that when a net force is applied to an object over a certain time interval, the force will cause a change in the object’s momentum. F∆t = ∆p = mv f – mv i force  time interval = change in momentum

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 1 Momentum and Impulse Chapter 6 Stopping times and distances depend on the impulse-momentum theorem. Force is reduced when the time interval of an impact is increased. Linear Momentum, continued

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Questions Which has more momentum, a 1-ton car moving at 100 mph or a 2-ton car moving at 50 mph? Does a moving object have impulse? Does a moving object have momentum? For the same force, which cannon imparts a greater impulse to a cannonball; a long cannon or a short one? Chapter 6 Section 1 Momentum and Impulse

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 6 Impulse-Momentum Theorem Section 1 Momentum and Impulse

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 6 Impulse-Momentum Theorem Section 1 Momentum and Impulse

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Imagine a car hitting a wall and coming to rest. The force on the car due to the wall is large (big F ), but that force only acts for a small amount of time (little t ). Now imagine the same car moving at the same speed but this time hitting a giant haystack and coming to rest. The force on the car is much smaller now (little F ), but it acts for a much longer time (big t ). In each case the impulse involved is the same since the change in momentum of the car is the same. Any net force, no matter how small, can bring an object to rest if it has enough time. A pole vaulter can fall from a great height without getting hurt because the mat applies a smaller force over a longer period of time than the ground alone would. Stopping Time F t = F t

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Impulse - Momentum Example A 1.3 kg ball is coming straight at a 75. kg soccer player at 13. m/s who kicks it in the exact opposite direction at 22. m/s with an average force of N. How long are his foot and the ball in contact?

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Practice Pg 201 (1, 3, 4) Pg 203 (2) Pg 204 (1- 5) Section 1 Momentum and Impulse Chapter 6

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Momentum is Conserved The 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. m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f total initial momentum = total final momentum Section 2 Conservation of Momentum Chapter 6

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Conservation of Momentum Chapter 6 Momentum is Conserved, continued Newton’s third law leads to conservation of momentum During the collision, the force exerted on each bumper car causes a change in momentum for each car. The total momentum is the same before and after the collision.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 6 Types of Collisions Section 3 Elastic and Inelastic Collisions

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Collisions Inelastic collision A collision in which two objects stick together after colliding and move together as one mass is called an inelastic collision. Conservation of momentum for an inelastic collision: m 1 v 1,i + m 2 v 2,i = (m 1 + m 2 )v f total initial momentum = total final momentum Section 3 Elastic and Inelastic Collisions Chapter 6

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 6 Perfectly Inelastic Collisions Section 3 Elastic and Inelastic Collisions

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Elastic Collisions Elastic Collision A collision in which the total momentum and the total kinetic energy are conserved is called an elastic collision. Objects bounce off of each other Momentum and Kinetic Energy Are Conserved in an Elastic Collision Section 3 Elastic and Inelastic Collisions Chapter 6

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Sample Problem 1 7 kg v = m/s A rifle fires a bullet into a giant slab of butter on a frictionless surface. The bullet penetrates the butter, but while passing through it, the bullet pushes the butter to the left, and the butter pushes the bullet just as hard to the right, slowing the bullet down. If the butter skids off at 4 cm/s after the bullet passes through it, what is the final speed of the bullet? 35 g 7 kg v = ? 35 g 4 cm/s continued on next slide

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Sample Problem 2 7 kg v = m/s 35 g Same as the last problem except this time it’s a block of wood rather than butter, and the bullet does not pass all the way through it. How fast do they move together after impact? v kg

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Sample Problem 4 before after 3 kg15 kg 10 m/s 6 m/s 3 kg 15 kg 4.5 m/sv?v? A crate of raspberry donut filling collides with a tub of lime Kool Aid on a frictionless surface. Which way on how fast does the Kool Aid rebound?

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Conceptual Question If a reckless ice skater collides with another skater who is standing on the ice, is it possible for both skaters to be at rest after the collision? A spacecraft undergoes a change of velocity when its rockets are fired. How does the spacecraft change velocity in empty space, where there is nothing for the gases emitted by the rockets to push against? Chapter 6 Section 2 Conservation of Momentum

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Story Open books to page 207 and read through the collision article. Section 2 Conservation of Momentum Chapter 6

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Practice Problems Pg 209 (1-4) Pg 211 (1-3) Chapter 6 Section 2 Conservation of Momentum

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Practice Problems Pg 214 (1-5) Pg 216 (1-3) Chapter 6 Section 3 Elastic and Inelastic Collisions

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Homework Problems Pg 211 (1-4) Pg 220 (1-5) Pg 223 (1-33 odd, 41, 44, 45, 49) Section 3 Elastic and Inelastic Collisions Chapter 6