One Dimensional Collisions
|
|
- Jerome Ward
- 5 years ago
- Views:
Transcription
1 One Diensional Collisions These notes will discuss a few different cases of collisions in one diension, arying the relatie ass of the objects and considering particular cases of who s oing. Along the way, I ll try to gie exaples appropriate to each type of collision. Ultiately, a force is a force is a force, and there s no FUNDAENTAL difference between the forces inoled when a ball and the Earth interact to ake the ball fall to the ground and the forces inoled when the Earth and the ball interact to ake the ball bounce. But in the latter case, the forces are BIG and interact oer a SHORT tie (we hae called these ipulsie forces. This is typically what is eant by the word collision and it does ake sense to kind of group the off by theseles. So we will. What is nice about the fact that the forces are BIG and act oer a SHORT tie is that they are often uch ore influential than all other forces for exaple, the forces inoled in the collision of a ball with a bat or when a firear is fired or when a neutron collides with a Uraniu nucleus (in a reactor or a bob are typically UCH greater than the weights of the objects. So it is usually the case that the effect of the other forces is inial during the collision. So, in collisions we will consider that there are no net, external forces. Then fro the Equation: r r PTOT FNET, EXT 0 ( t we can conclude that the total oentu does NOT change that is, the total oentu before the collision will be the sae as the total oentu after the collision. So consider the siplest collision iaginable that is not triial two objects oing along a line. (In general, ore objects in ore than one diension ake the proble ore coplicated, but do not change the physics inoled the sorts of conclusions we will draw do not depend on the collision being one-diensional. Consider the drawing: Before V V After It shows an object of ass oing at speed colliding with an object of ass oing at speed V. After the collision, the first object of ass is oing at speed and the second object of ass is oing at speed V. Despite the drawing, we ake no assuptions about which object is ore assie (in fact, in the exaples we ll consider all different possibilities. Knowing that the total oentu is consered, we can write that the oentu before is equal to the oentu after:
2 PTOT, Before PTOT, After ( + V + V ' In these sorts of probles, you re interested in what happened after the collisions that is, you want and V. As things stand, we hae only one equation and two unknowns. To sole for AND V, we need another equation (or so say the atheaticians. So we further classify interactions in ters of what happens to the kinetic energy of the two objects. In general, soe fraction of the kinetic energy will be lost, anywhere fro none (a perfectly elastic collision to the ost possible, gien that oentu ust be consered (a perfectly INelastic collision. We will consider the two extrees and along the way I ll say a few words about the general case. Perfectly Inelastic collision In this case, the two objects stick and oe at the sae elocity after the collision: V. It is straightforward to find the final elocity using Eq. : + V V ' (3 + An exaple of this kind of collision would be ud splattering on a car window or a theral neutron colliding with a uraniu nucleus or a eteor colliding with the Earth. As we will see, there is a loss of kinetic energy in this type of collision for the ud on the window, the splattering takes energy and there is soe heat generated. In the uraniu nucleus, the lost kinetic energy causes the nucleus to start sloshing around until it breaks in half (this is called fission. With a eteor colliding with the Earth, the lost kinetic energy showed up as a assie explosion that caused the extinction of the dinosaurs. As an exaple, suppose we ARE talking about the collision of a assie, house-sized eteor with the Earth. Suppose that the Earth and the eteor collide head on, going about the sae speed. (In fact, the eteor will be going about 40% faster, as you can calculate yourself see p. 60 and 93 of your text. Also, there s no way to tell yet whether the collision was head-on, fro the side or what. But we can proceed nonetheless. That is, we assue V - (sae speed, but in opposite directions. Then Eq. 3 tells us that the final speed is: + V V ' V (4 + + Considering that the eteor has a ass of aybe 000 tons ( 0 6 kg and the Earth a ass of about 0 5 kg, it s pretty clear that the final speed will be about equal to the speed the Earth was going before the collision (uch like a fly hitting a windshield, only ore so. We won t do the calculation here in the interest of tie, but a firear can be considered an inelastic collision in reerse the kinetic energy is created by the exploding gasses rather than lost and the oentu is consered when the recoil of the firear balances the oentu of the bullet. A couple of other exaples that you should do yourself are: Suppose one object (say is initially not oing (V0. Then the final elocity is: V ' (5 + +
3 And suppose further that the stationary object is uch ore assie than the oing object ( << this is a tiny piece of clay colliding with the wall of a building. Then the final elocity is: ' V ' << (6 That is, as we know, the cobined object will oe away at a elocity UCH less than the initial elocity of the saller object. On the other hand, suppose that the stationary object is uch LESS assie ( >> this is a fly being hit by a car. Then Eq. 5 becoes: ' V ' (7 + That is, the cobined object goes about the speed of the initially oing object (as would be expected. We re really done here (since we know how to calculate the final elocities of the colliding objects but we can consider a couple of other ites while we re here. One is the idea of the center of ass of the syste. That s a little easier to deal with since we only hae two objects. We e concluded in class that P TOT TOT CO, so it s pretty easy to sole that for the center of ass of the syste: PTOT + V CO (8 TOT + where I e used the oentu before the collision. If one of the objects has a UCH larger oentu than the other, we can see that the elocity of the center of ass will be about equal to the elocity of that object (the Earth and the eteor, for exaple. But note that if the total oentu is consered, then the elocity of the center of ass ust be the sae (if P TOT TOT CO, and P TOT is constant, then CO ust be constant and so we should get the sae answer if we calculate CO after the collision. So let s do it: PTOT + V ' + + V CO (9 TOT So, as adertised, we see that the elocity of the center of ass is the sae before and after the collision. But een ore, we see that the elocity of the center of ass is the sae as the speed of the cobined particle after the collision (which akes sense if there s only one thing, the elocity of the center of ass ust be the sae as the elocity of that thing. The second thing to consider is the kinetic energy lost in an elastic collision (appropriate since we will next consider elastic collisions in which the kinetic energy IS consered. This is typically done by considering the fraction of kinetic energy lost and this is historically labeled Q : KEi KE Q KE i f + V V ' + V ' + V + V We can factor the ters in the nuerator in the following way: (0
4 ( ( + + ( V V '( V V ' + V V ' + ( Fro conseration of oentu, we know that: ( ( V V + V + V ' so that ' ( And so the nuerator can be written: ( ( + + ( V V '( V + V ' ( ( + V V ' (3 And so the alue of Q can be written: ( ( [ V + ( V '] Q (4 + V This is a ery general expression that is, we haen t said anything about what kind of collision is inoled. We ll use it later to consider elastic collisions, but for now we ll consider what happens in an inelastic collision. In that case, we hae that V and is gien by equation 7. So, the expression for Q becoes: + V ( V ( V Q + + (5 + V + V For the exaples discussed earlier, we can calculate Q. For the eteor striking Earth, we hae -V: Q + + (6 ( ( 4 ( Since <<, we can see that the fraction of kinetic energy lost is tiny. This akes sense the VAST ajority of the kinetic energy is the kinetic energy of the Earth, which really isn t affected. But it turns out that four ties the kinetic energy of the eteor is dissipated in the collision: K lost Q K 4 i 4 + V ( ( + 4 ( 4 Finally, fro Equation 6 we see that the axiu loss of kinetic energy occurs when the asses are equal and the objects are oing in opposite directions. This is the reason that particle physicists sash atos by running the into one another going in opposite directions this gies the axiu aount of kinetic energy to ake new particles. Perfectly Elastic Collision In this type of collision, the oentu is still consered, so we hae Equation ( as one equation to sole for and V. And we know that kinetic energy is consered, so this is another (7
5 equation. But we can short cut a LOT of algebra because we already did it. Consider Equation (4. This is the general expression for Q. But for a perfectly elastic collision, we know that Q 0. So we can get the second equation for and V fro there. If Q 0, then it ust be that either (both objects oe at the sae speed in the sae direction and therefore NEVER collide OR: ( V + ( V ' 0 (8 which gies us two equations to sole for and V. So let s. I can sole Equation (8 for V : V ' V + (9 Substitute this into Equation ( to get: ( + V + V + ' (0 Soling this for, we get: ( + V ( And plugging this into Equation (9, we get: ( V + V ' ( Again, we re basically done, as we hae the elocity for both particles after the collision in ters of the initial elocities and the asses. But we can consider a few exaples: Elastic collision one object initially still: Suppose one object is standing still (V0. Then the elocities reduce to: V ' ( If the asses are equal (, then these elocities becoe: V ' ( 0 In this case, the speeds are switched (the initially otionless object oes at the speed of the oing object and the initially oing object stops. This describes a gae of pool the cue ball oes toward the object ball, strikes it and stops as the object ball goes into the hole. (It also shows the answer to one of your HW probles. If the otionless object is ery assie ( >>, then: (3 (4
6 V ' ( ( ( + << In this case, the sall object reerses its elocity (the sae speed in the opposite direction and the large object oes a little (just enough to consere oentu. An exaple would be a superball hitting the Earth. Finally, suppose the initially otionless object is ery sall ( << : V ' ( ( ( The large oing object continues pretty uch unaffected and the sall otionless object bounces at twice the elocity. If a train with a cowcatcher hits a car, the car will bounce away at a speed faster than that of the train (although this is NOT likely to be perfectly elastic. Now suppose that the objects trael at the sae speed, but in opposite directions: Elastic collision objects trael in opposite directions: Traelling at the sae speed but in opposite directions iplies -V: V ' ( + ( V + V Suppose the asses are equal (: 3 ( + ( 3 3 V ' V ( + ( 3 ( In this case, both objects bounce back in the opposite direction with the sae speed. Suppose one object is uch ore assie than the other (it doesn t atter which, as you should proe suppose << : V ' V Here (again the assie object is largely unaffected by the collision, but the light object bounces back at 3 ties the speed. This describes an experient you can perfor balance a tennis ball or a superball on a basketball and then drop the together. The effect is draatic. (5 (6 (7 (8 (9
Momentum, p = m v. Collisions and Work(L8) Crash! Momentum and Collisions. Conservation of Momentum. elastic collisions
Collisions and Work(L8) Crash! collisions can be ery coplicated two objects bang into each other and exert strong forces oer short tie interals fortunately, een though we usually do not know the details
More informationConservation of Momentum
Conseration of Moentu We left off last with the idea that when one object () exerts an ipulse onto another (), exerts an equal and opposite ipulse onto. This happens in the case of a classic collision,
More informationMomentum, p. Crash! Collisions (L8) Momentum is conserved. Football provides many collision examples to think about!
Collisions (L8) Crash! collisions can be ery coplicated two objects bang into each other and exert strong forces oer short tie interals fortunately, een though we usually do not know the details of the
More informationPage 1. Physics 131: Lecture 16. Today s Agenda. Collisions. Elastic Collision
Physics 131: Lecture 16 Today s Agenda Elastic Collisions Definition Exaples Work and Energy Definition of work Exaples Physics 01: Lecture 10, Pg 1 Collisions Moentu is alost always consered during as
More informationChapter 9 Centre of Mass and Linear Momentum
Chater 9 Centre o Mass and Linear Moentu Centre o ass o a syste o articles / objects Linear oentu Linear oentu o a syste o articles Newton s nd law or a syste o articles Conseration o oentu Elastic and
More informationPage 1. t F t m v. N s kg s. J F t SPH4U. From Newton Two New Concepts Impulse & Momentum. Agenda
SPH4U Agenda Fro Newton Two New Concepts Ipulse & oentu Ipulse Collisions: you gotta consere oentu! elastic or inelastic (energy consering or not) Inelastic collisions in one diension and in two diensions
More informationChapter 7. Impulse and Momentum
Chapter 7 Ipulse and Moentu 7. The Ipulse-Moentu Theore There are any situations when the force on an object is not constant. 7. The Ipulse-Moentu Theore DEFINITION OF IMPULSE The ipulse of a force is
More information8.012 Physics I: Classical Mechanics Fall 2008
MIT OpenCourseWare http://ocw.it.edu 8.012 Physics I: Classical Mechanics Fall 2008 For inforation about citing these aterials or our Ters of Use, isit: http://ocw.it.edu/ters. MASSACHUSETTS INSTITUTE
More informationPhysics 201, Lecture 15
Physics 0, Lecture 5 Today s Topics q More on Linear Moentu And Collisions Elastic and Perfect Inelastic Collision (D) Two Diensional Elastic Collisions Exercise: Billiards Board Explosion q Multi-Particle
More informationincreases. In part (b) the impulse and initial momentum are in opposite directions and the velocity decreases.
8IDENTIFY and SET U: p = K = EXECUTE: (a) 5 p = (, kg)( /s) = kg /s 5 p kg /s (b) (i) = = = 6 /s (ii) kg =, so T T SUV SUV, kg ( /s) 68 /s T SUV = T = = SUV kg EVALUATE:The SUV ust hae less speed to hae
More informationUNIT HOMEWORK MOMENTUM ANSWER KEY
UNIT HOMEWORK MOMENTUM ANSWER KEY MOMENTUM FORMULA & STUFF FROM THE PAST: p = v, TKE = ½v 2, d = v t 1. An ostrich with a ass of 146 kg is running to the right with a velocity of 17 /s. a. Calculate the
More informationToday s s topics are: Collisions and Momentum Conservation. Momentum Conservation
Today s s topics are: Collisions and P (&E) Conservation Ipulsive Force Energy Conservation How can we treat such an ipulsive force? Energy Conservation Ipulsive Force and Ipulse [Exaple] an ipulsive force
More informationMomentum. February 15, Table of Contents. Momentum Defined. Momentum Defined. p =mv. SI Unit for Momentum. Momentum is a Vector Quantity.
Table of Contents Click on the topic to go to that section Moentu Ipulse-Moentu Equation The Moentu of a Syste of Objects Conservation of Moentu Types of Collisions Collisions in Two Diensions Moentu Return
More informationLecture 6. Announcements. Conservation Laws: The Most Powerful Laws of Physics. Conservation Laws Why they are so powerful
Conseration Laws: The Most Powerful Laws of Physics Potential Energy gh Moentu p = + +. Energy E = PE + KE +. Kinetic Energy / Announceents Mon., Sept. : Second Law of Therodynaics Gie out Hoework 4 Wed.,
More informationChapter 7. Impulse and Momentum
Chapter 7 Ipulse and Moentu 7. The Ipulse-Moentu Theore 7. The Ipulse-Moentu Theore There are any situations when the force on an object is not constant. 7. The Ipulse-Moentu Theore DEFINITION OF IMPULSE
More informationPhysics 140 D100 Midterm Exam 2 Solutions 2017 Nov 10
There are 10 ultiple choice questions. Select the correct answer for each one and ark it on the bubble for on the cover sheet. Each question has only one correct answer. (2 arks each) 1. An inertial reference
More informationChapter 7 Impulse and Momentum. So far we considered only constant force/s BUT There are many situations when the force on an object is not constant
Chapter 7 Ipulse and Moentu So far we considered only constant force/s BUT There are any situations when the force on an object is not constant Force varies with tie 7. The Ipulse-Moentu Theore DEFINITION
More informationMomentum. Momentum. Momentum. January 25, momentum presentation Table of Contents. Momentum Defined. Grade:«grade»
oentu presentation 2016 New Jersey Center for Teaching and Learning Progressive Science Initiative This aterial is ade freely available at wwwnjctlorg and is intended for the non coercial use of students
More informationPhysics 11 HW #7 Solutions
hysics HW #7 Solutions Chapter 7: Focus On Concepts: 2, 6, 0, 3 robles: 8, 7, 2, 22, 32, 53, 56, 57 Focus On Concepts 7-2 (d) Moentu is a ector quantity that has a agnitude and a direction. The agnitudes
More informationConservation of Linear Momentum, Collisions
Conseration of Linear Momentum, Collisions 1. 3 kg mass is moing with an initial elocity i. The mass collides with a 5 kg mass m, which is initially at rest. Find the final elocity of the masses after
More informationChapter 7 Impulse and Momentum. So far we considered only constant force/s BUT There are many situations when the force on an object is not constant
Chapter 7 Ipulse and Moentu So far we considered only constant force/s BUT There are any situations when the force on an object is not constant JUST IN TIME TEACHING E-ail or bring e your questions prior
More informationPHYSICS. Chapter 11 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 11 Lecture RANDALL D. KNIGHT Chapter 11 Impulse and Momentum IN THIS CHAPTER, you will learn to use the concepts of impulse and momentum.
More informationbefore the collision and v 1 f and v 2 f after the collision. Since conservation of the linear momentum
Lecture 7 Collisions Durin the preious lecture we stared our discussion of collisions As it was stated last tie a collision is an isolated eent in which two or ore odies (the collidin odies) exert relatiely
More informationPhysics Circular Motion: Energy and Momentum Conservation. Science and Mathematics Education Research Group
F FA ACULTY C U L T Y OF O F EDUCATION E D U C A T I O N Departent of Curriculu and Pedagogy Physics Circular Motion: Energy and Moentu Conservation Science and Matheatics Education Research Group Supported
More informationChapter 1. Momentum. Fun and physics on screen
Chapter 1 Moentu Objectives e-learning Fun and physics on screen If you play coputer gaes (Figure 1.1) you will be failiar with the way in which characters ove about the screen. Cars accelerate and decelerate
More informationCHAPTER 7: Linear Momentum
CHAPTER 7: Linear Moentu Solution Guide to WebAssign Probles 7.1 [1] p v ( 0.08 kg) ( 8.4 s) 0.4 kg s 7. [] Fro Newton s second law, p Ft. For a constant ass object, p v. Equate the two expression for
More informationPhysics Momentum: Collisions
F A C U L T Y O F E D U C A T I O N Departent o Curriculu and Pedagogy Physics Moentu: Collisions Science and Matheatics Education Research Group Supported by UBC Teaching and Learning Enhanceent Fund
More informationConcepTest PowerPoints
ConcepTest PowerPoints Chapter 7 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for
More informationGeneral Physics I Momentum
General Physics I Momentum Linear Momentum: Definition: For a single particle, the momentum p is defined as: p = mv (p is a vector since v is a vector). So p x = mv x etc. Units of linear momentum are
More informationPhysically Based Modeling CS Notes Spring 1997 Particle Collision and Contact
Physically Based Modeling CS 15-863 Notes Spring 1997 Particle Collision and Contact 1 Collisions with Springs Suppose we wanted to ipleent a particle siulator with a floor : a solid horizontal plane which
More informationPhysics 231 Lecture 13
Physics 3 Lecture 3 Mi Main points it o td today s lecture: Elastic collisions in one diension: ( ) v = v0 + v0 + + ( ) v = v0 + v0 + + Multiple ipulses and rocket propulsion. F Δ t = Δ v Δ v propellant
More informationSOLUTIONS TO CONCEPTS CHAPTER 9
SOUTIONS TO CONCEPTS CHPTER 9. kg, kg, kg, x 0, x, x / y 0, y 0, y / The position of centre of ass is C. x x x y y y, ( 0) ( ) ( / ) ( 0) ( 0) ( (, 7, fro the point B. / )). et be the origin of the syste
More informationMomentum and Collisions
Momentum and Collisions Objectives: You Should Be Able To: Define and give examples of impulse and momentum along with appropriate units. Write and apply a relationship between impulse and momentum in
More informationPS 11 GeneralPhysics I for the Life Sciences
PS GeneralPhysics I for the Life Sciences W O R K N D E N E R G Y D R. E N J M I N C H N S S O C I T E P R O F E S S O R P H Y S I C S D E P R T M E N T J N U R Y 0 4 Questions and Probles for Conteplation
More informationKinetic Molecular Theory of Ideal Gases
Lecture -3. Kinetic Molecular Theory of Ideal Gases Last Lecture. IGL is a purely epirical law - solely the consequence of experiental obserations Explains the behaior of gases oer a liited range of conditions.
More informationYour Thoughts. What is the difference between elastic collision and inelastic collision?
Your Thoughts This seemed pretty easy...before we got the checkpoint questions What is the difference between elastic collision and inelastic collision? The most confusing part of the pre lecture was the
More informationPhysics Chapter 6. Momentum and Its Conservation
Physics Chapter 6 Moentu and Its Conservation Linear Moentu The velocity and ass of an object deterine what is needed to change its otion. Linear Moentu (ρ) is the product of ass and velocity ρ =v Unit
More informationQ5 We know that a mass at the end of a spring when displaced will perform simple m harmonic oscillations with a period given by T = 2!
Chapter 4.1 Q1 n oscillation is any otion in which the displaceent of a particle fro a fixed point keeps changing direction and there is a periodicity in the otion i.e. the otion repeats in soe way. In
More informationNotes Momentum. Momentum and Impulse. - The product (multiplication) of an objects mass and velocity is called momentum.
Notes Momentum Momentum and Impulse - The product (multiplication) of an objects mass and velocity is called momentum. Momentum is the energy of motion of an object. Momentum is represented by the letter.
More informationCHAPTER 7 TEST REVIEW -- MARKSCHEME
AP PHYSICS Nae: Period: Date: Points: 53 Score: IB Curve: DEVIL PHYSICS BADDEST CLASS ON CAMPUS 50 Multiple Choice 45 Single Response 5 Multi-Response Free Response 3 Short Free Response 2 Long Free Response
More informationConservation of Momentum
Conservation of Momentum Law of Conservation of Momentum The sum of the momenta before a collision equal the sum of the momenta after the collision in an isolated system (=no external forces acting).
More informationBALLISTIC PENDULUM. EXPERIMENT: Measuring the Projectile Speed Consider a steel ball of mass
BALLISTIC PENDULUM INTRODUCTION: In this experient you will use the principles of conservation of oentu and energy to deterine the speed of a horizontally projected ball and use this speed to predict the
More informationKinetic Molecular Theory of. IGL is a purely empirical law - solely the
Lecture -3. Kinetic Molecular Theory of Ideal Gases Last Lecture. IGL is a purely epirical law - solely the consequence of experiental obserations Explains the behaior of gases oer a liited range of conditions.
More informationMomentum Practice Problems
Momentum Practice Problems PSI AP Physics C Name Multiple Choice 1. A steel ball and a piece of clay have equal mass. They are dropped from the same height on a horizontal steel platform. The ball bounces
More informationMomentum. Conservation of Linear Momentum. Slide 1 / 140 Slide 2 / 140. Slide 3 / 140. Slide 4 / 140. Slide 6 / 140. Slide 5 / 140.
Slide 1 / 140 Slide 2 / 140 Moentu www.njctl.org Slide 3 / 140 Slide 4 / 140 Table of Contents Click on the topic to go to that section Conservation of Linear Moentu Ipulse - Moentu Equation Collisions
More informationA B B A. the speed of the bat doesn t change significantly during the collision. Then the velocity of the baseball after being hit is v
CHPTER 7: Linear oentu nswers to Questions. For oentu to be consered, the syste under analysis ust be closed not hae any forces on it fro outside the syste. coasting car has air friction and road friction
More informationWhat is momentum? Inertia in Motion.
What is momentum? Inertia in Motion. p = mv From Newton s 2 nd Law: F = ma = dv d( mv) m = dt dt F = dp dt The time rate of change of the linear momentum of a particle is equal to the net force acting
More informationTest, Lesson 4 Energy-Work-Power- Answer Key Page 1
Test, Lesson 4 Energy-Work-Power- Answer Key Page 1 1. What is the axial height for the ond hup on a roller coaster if the roller coaster is traveling at 108 k just before hr clibing the ond hup? The ond
More informationNote-A-Rific: Mechanical
Note-A-Rific: Mechanical Kinetic You ve probably heard of inetic energy in previous courses using the following definition and forula Any object that is oving has inetic energy. E ½ v 2 E inetic energy
More information26 Impulse and Momentum
6 Ipulse and Moentu First, a Few More Words on Work and Energy, for Coparison Purposes Iagine a gigantic air hockey table with a whole bunch of pucks of various asses, none of which experiences any friction
More informationName Class Date. two objects depends on the masses of the objects.
CHAPTER 12 2 Gravity SECTION Forces KEY IDEAS As you read this section keep these questions in ind: What is free fall? How are weight and ass related? How does gravity affect the otion of objects? What
More informationNational 5 Summary Notes
North Berwick High School Departent of Physics National 5 Suary Notes Unit 3 Energy National 5 Physics: Electricity and Energy 1 Throughout the Course, appropriate attention should be given to units, prefixes
More informationYou are given two carts, A and B. They look identical, and you are told they are made of the same material. You put A at rest on a low-friction
You are given two carts, A and B. They look identical, and you are told they are made of the same material. You put A at rest on a low-friction track, then send B towards it to the right. After the collision,
More informationMomentum. Conservation of Linear Momentum. Slide 1 / 140 Slide 2 / 140. Slide 3 / 140. Slide 4 / 140. Slide 6 / 140. Slide 5 / 140.
Slide 1 / 140 Slide 2 / 140 Moentu www.njctl.org Slide 3 / 140 Slide 4 / 140 Table of Contents Click on the topic to go to that section Conservation of Linear Moentu Ipulse - Moentu Equation Collisions
More informationLecture 7 - Momentum. A Puzzle... Momentum. Basics (1)
Lecture 7 - omentum A Puzzle... An Experiment on Energy The shortest configuration of string joining three given points is the one where all three angles at the point of intersection equal 120. How could
More informationSPH4U. Conservation of Energy. Review: Springs. More Spring Review. 1-D Variable Force Example: Spring. Page 1. For a spring we recall that F x = -kx.
-D Variable Force Exaple: Spring SPH4U Conseration of Energ For a spring we recall that F x = -kx. F(x) x x x relaxe position -kx F = - k x the ass F = - k x Reiew: Springs Hooke s Law: The force exerte
More information4 Conservation of Momentum
hapter 4 oneration of oentu 4 oneration of oentu A coon itake inoling coneration of oentu crop up in the cae of totally inelatic colliion of two object, the kind of colliion in which the two colliding
More informationLinear Momentum and Collisions Conservation of linear momentum
Unit 4 Linear omentum and Collisions 4.. Conseration of linear momentum 4. Collisions 4.3 Impulse 4.4 Coefficient of restitution (e) 4.. Conseration of linear momentum m m u u m = u = u m Before Collision
More informationPhys101 Lectures 13, 14 Momentum and Collisions
Phs0 Lectures 3, 4 Moentu and ollisions Ke points: Moentu and ipulse ondition for conservation of oentu and wh How to solve collision probles entre of ass Ref: 7-,,3,4,5,6,7,8,9,0. Page Moentu is a vector:
More informationPhysics 10 Lecture 6A. "And in knowing that you know nothing, that makes you the smartest of all. --Socrates
Physics 10 Lecture 6A "And in knowing that you know nothing, that makes you the smartest of all. --Socrates Momentum Which is harder to stop a small ball moving at 1 m/s or a car moving at 1 m/s? Obviously
More informationCHAPTER 7 IMPULSE AND MOMENTUM
CHAPTER 7 IMPULSE AND MOMENTUM PROBLEMS 1. SSM REASONING The ipulse that the olleyball player applies to the ball can be ound ro the ipulse-oentu theore, Equation 7.4. Two orces act on the olleyball while
More informationCHAPTER 1 MOTION & MOMENTUM
CHAPTER 1 MOTION & MOMENTUM SECTION 1 WHAT IS MOTION? All atter is constantly in MOTION Motion involves a CHANGE in position. An object changes position relative to a REFERENCE POINT. DISTANCE is the total
More informationXI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K. https://promotephysics.wordpress.com
XI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K affan_414@live.co https://prootephysics.wordpress.co [MOTION] CHAPTER NO. 3 In this chapter we are going to discuss otion in one diension in which we
More informationPhysic 602 Conservation of Momentum. (Read objectives on screen.)
Physic 602 Conservation of Momentum (Read objectives on screen.) Good. You re back. We re just about ready to start this lab on conservation of momentum during collisions and explosions. In the lab, we
More informationFrames of Reference, Energy and Momentum, with
Frames of Reference, Energy and Momentum, with Interactie Physics Purpose: In this lab we will use the Interactie Physics program to simulate elastic collisions in one and two dimensions, and with a ballistic
More information2. REASONING According to the impulse-momentum theorem, the rocket s final momentum mv f
CHAPTER 7 IMPULSE AND MOMENTUM PROLEMS. REASONING According to the ipulse-oentu theore, the rocket s inal oentu diers ro its initial oentu by an aount equal to the ipulse ( ΣF ) o the net orce eerted on
More informationENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 2 LINEAR IMPULSE AND MOMENTUM
ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D5 TUTORIAL LINEAR IMPULSE AND MOMENTUM On copletion of this ttorial yo shold be able to do the following. State Newton s laws of otion. Define linear
More informationCollisions in 1- and 2-D
Collisions in 1- and 2-D Momentum and Energy Conservation Physics 109 Experiment Number 7 2017 Outline Brief summary of Binary Star Experiment Some thoughts on conservation principles Description of the
More informationT = 2.34x10 6 s = 27.2days.
Sole the following probles in the space proided Use the back of the page if needed Each proble is worth 10 points You ust show your work in a logical fashion starting with the correctly applied and clearly
More informationWe last left off by talking about how the area under a force vs. time curve is impulse.
Lecture 11 Ipulse and Moentu We last left off by talking about how the area under a force vs. tie curve is ipulse. Recall that for our golf ball we had a strongly peaked force curve: F F avg t You have
More informationDonald Fussell. October 28, Computer Science Department The University of Texas at Austin. Point Masses and Force Fields.
s Vector Moving s and Coputer Science Departent The University of Texas at Austin October 28, 2014 s Vector Moving s Siple classical dynaics - point asses oved by forces Point asses can odel particles
More informationElastic collisions. Objectives. Physics terms. Assessment. Review: conservation laws. Equations 5/14/14. Define and describe an elastic collision.
Elastic collisions Objectives Define and describe an elastic collision. Describe the possible outcomes that result from the collision of one moving ball with one stationary ball when their masses are equal
More information5.1 m is therefore the maximum height of the ball above the window. This is 25.1 m above the ground. (b)
.6. Model: This is a case of free fall, so the su of the kinetic and gravitational potential energy does not change as the ball rises and falls. The figure shows a ball s before-and-after pictorial representation
More informationLecture 11. Linear Momentum and Impulse. Collisions.
Lecture 11 Linear Momentum and Impulse. Collisions. Momentum and Newton s Second Law F net = m a= m Δ v Δ t = Δ (m v ) Δ t = Δ p Δ t Linear momentum p = m v Newton s second law in terms of linear momentum:
More information10/11/11. Physics 101 Tuesday 10/11/11 Class 14" Chapter " Inelastic collisions" Elastic collisions" Center of mass"
Consider the following situations and possible isolated systems: Physics 101 Tuesday Class 14" Chapter 9.5 9.7" Inelastic collisions" Elastic collisions" Center of mass" Two cars on an icy road collide.
More informationMomentum Energy Angular Momentum
Notes 8 Impulse and Momentum Page 1 Impulse and Momentum Newton's "Laws" require us to follow the details of a situation in order to calculate properties of the system. Is there a simpler way? CONSERVATION
More informationFOCUS ON CONCEPTS Section 7.1 The Impulse Momentum Theorem
WEEK-6 Recitation PHYS 3 FOCUS ON CONCEPTS Section 7. The Impulse Momentum Theorem Mar, 08. Two identical cars are traeling at the same speed. One is heading due east and the other due north, as the drawing
More informationCh 7 Impulse-Momentum Theorem, Conservation of Momentum, and Collisions
Ch 7 Impulse-Momentum Theorem, Conservation of Momentum, and Collisions Momentum and its relation to force Momentum describes an object s motion. Linear momentum is the product of an object s mass and
More informationSome Perspective. Forces and Newton s Laws
Soe Perspective The language of Kineatics provides us with an efficient ethod for describing the otion of aterial objects, and we ll continue to ake refineents to it as we introduce additional types of
More informationLesson 24: Newton's Second Law (Motion)
Lesson 24: Newton's Second Law (Motion) To really appreciate Newton s Laws, it soeties helps to see how they build on each other. The First Law describes what will happen if there is no net force. The
More informationAlgebra Based Physics
1 Algebra Based Physics Momentum 2016 01 20 www.njctl.org 2 Momentum Click on the topic to go to that section Momentum Impulse Momentum of a System of Objects Conservation of Momentum Inelastic Collisions
More informationDescription: Conceptual: A bullet embeds in a stationary, frictionless block: type of collision? what is conserved? v_final?
Chapter 8 [ Edit ] Overview Suary View Diagnostics View Print View with Answers Chapter 8 Due: 11:59p on Sunday, October 23, 2016 To understand how points are awarded, read the Grading Policy for this
More information1 A freight car of mass 20,000 kg moves along a frictionless level railroad track with a constant speed of 15 m/s. What is the momentum of the car?
Slide 1 / 26 1 freight car of mass 20,000 kg moves along a frictionless level railroad track with a constant speed of 15 m/s. What is the momentum of the car? 30,000 kg m/s 3,000 kg m/s 300,000 kg m/s
More informationUNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics
UNIVERSITY OF SASKATCHEWAN Departent of Physics and Engineering Physics 017 Saskatchewan High School Physics Scholarship Copetition Wednesday May 10, 017 Tie allowed: 90 inutes This copetition is based
More informationMomentum Conceptual Questions. 1. Which variable has more impact on an object s motion? Its mass or its velocity?
AP Physics I Momentum Conceptual Questions 1. Which variable has more impact on an object s motion? Its mass or its velocity? 2. Is momentum a vector or a scalar? Explain. 3. How does changing the duration
More informationThe product of force and displacement ( in the direction of force ), during which the force is acting, is defined as work.
5 WORK, ENERGY ND POWER Page 5. Work The product of force and displaceent ( in the direction of force ), during which the force is acting, is defined as work. When N force is applied on a particle and
More informationKey Terms Electric Potential electrical potential energy per unit charge (JC -1 )
Chapter Seenteen: Electric Potential and Electric Energy Key Ter Electric Potential electrical potential energy per unit charge (JC -1 ) Page 1 of Electrical Potential Difference between two points is
More information(k = force constant of the spring)
Lecture 10: Potential Energy, Momentum and Collisions 1 Chapter 7: Conservation of Mechanical Energy in Spring Problems The principle of conservation of Mechanical Energy can also be applied to systems
More information1) To Work or Not to Work
1) To Work or Not to Work Is it possible to do work on an object that remains at rest? 1) yes 2) no 1) To Work or Not to Work Is it possible to do work on an object that remains at rest? 1) yes 2) no Work
More informationChapter 11 Collision Theory
Chapter Collision Theory Introduction. Center o Mass Reerence Frame Consider two particles o masses m and m interacting ia some orce. Figure. Center o Mass o a system o two interacting particles Choose
More informationChapter 6 - Linear Momemtum and Collisions
Name Date Chapter 6 - Linear Momemtum and Collisions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) What is the SI unit of momentum? A) N/s B)
More informationNB1140: Physics 1A - Classical mechanics and Thermodynamics Problem set 2 - Forces and energy Week 2: November 2016
NB1140: Physics 1A - Classical echanics and Therodynaics Proble set 2 - Forces and energy Week 2: 21-25 Noveber 2016 Proble 1. Why force is transitted uniforly through a assless string, a assless spring,
More informationPhysics 11 Fall 2012 Practice Problems 4
Physics 11 Fall 2012 Practice Problems 4 1. Under what conditions can all the initial kinetic energy of an isolated system consisting of two colliding objects be lost in a collision? Explain how this result
More informationThe total momentum in any closed system will remain constant.
The total momentum in any closed system will remain constant. When two or more objects collide, the collision does not change the total momentum of the two objects. Whatever momentum is lost by one object
More informationAP Physics 1 Momentum
AP Physics 1 Momentum 2017-07-20 www.njctl.org Table of Contents Click on the topic to go to that section Momentum Impulse-Momentum Equation The Momentum of a System of Objects Conservation of Momentum
More informationThe SI units of mass are kilograms (kg) and of velocity are meters / second (m/s). Therefore, the units of momentum are kg m/s.
Momentum Introduction As was pointed out in the previous chapter, some of the most powerful tools in physics are based on conservation principles. The idea behind a conservation principle is that there
More informationPer 9 10 Momentum_Presentation.notebook. January 20, Momentum.
Momentum www.njctl.org 1 Momentum Click on the topic to go to that section Momentum Impulse Momentum of a System of Objects Conservation of Momentum Inelastic Collisions and Explosions Elastic Collisions
More informationApplied Physics I (Phys 182)
Applied Physics I (Phys 182) Dr. Joseph J. Trout E-ail: joseph.trout@drexel.edu Cell: (610)348-6495 Office: Disque 902 1 Moentu Ipulse Conservation of Moentu Explosions Inelastic Collisions Elastic Collisions
More informationKinetic Theory of Gases: Elementary Ideas
Kinetic Theory of Gases: Eleentary Ideas 17th February 2010 1 Kinetic Theory: A Discussion Based on a Siplified iew of the Motion of Gases 1.1 Pressure: Consul Engel and Reid Ch. 33.1) for a discussion
More informationCenter of Mass & Linear Momentum
PHYS 101 Previous Exam Problems CHAPTER 9 Center of Mass & Linear Momentum Center of mass Momentum of a particle Momentum of a system Impulse Conservation of momentum Elastic collisions Inelastic collisions
More information