Chapters 9-10 Impulse and Momentum
|
|
- Sydney Lester
- 5 years ago
- Views:
Transcription
1 Chapters 9-10 Impulse and Momentum Momentum Concept Newton s 2 nd Law restated Conservation of momentum Impulse. Impulse-Momentum Theorem Collisions 1D inelastic and elastic collisions 2D collisions
2 1. Quantity of Motion A historical preamble Query: How can one quantify motion? Is the mere velocity enough? Historically, philosophers of nature quantified motion using the intuitive kinematic concept of velocity: however, simple experiments of removing movement show that the amount of moving substance, that is mass, must play a role in defining the amount of motion Ex: Consider two balls with the same size but different mass. When launched with the same speed, the heavier ball will compress a spring more Wood Steel v 0 v 0 v 0 This became obvious by the XVII century, with the tendency to look for the causal emergence of mechanical phenomena based on universal principles, such as conservation laws Descartes was the first to notice that, if a quantity of motion comprises both velocity v and mass m, the product mv is preserved in collisions, while Huygens suggested that to solve any collisions the quantity can be also negative, that is, it depends on direction Leibniz had an alternative approach associating motion with the product mv 2 related to the modern concept of kinetic energy Newton adopted the concept of quantity of motion, and built his mechanics as a mathematical compilation of how it can be changed in proportion to the applied forces
3 Momentum Its Relation to Force Def: The translational momentum of a particle of mass m moving with a velocity v is a vector given by the product of mass and velocity: p mv m p kg m s or Ns SI p In modern formalism, Newton stated his 2 nd law in terms of momentum: the net force applied to an object is equal to the rate of change of its momentum This is equivalent with the popular form F = ma only when the mass of the moving particle is constant: m dp d mv dv dm dm F m v ma v dt dt dt dt dt Ex: 1D uniform motion: Consider a particle of mass m moving in a straight displacement Δx, acted for a time Δt by a constant force F parallel with the motion. F F p0 mv0 Δx = x 1 x 0 p mv Δt = t x t 0, x 1 t 0 0 t 1, x 1 p F Ft p p0 Ft mv1 mv0 t By Newton s 2 nd Law, the momentum will increased as given by F dp dt
4 Momentum Conservation of Net Momentum Newton s 2 nd law in terms of momentum can be used to demonstrate that the net momentum is conserved within isolated systems In order to understand how momentum is conserved, recall the concept of internal forces: forces between the parts of a system to be contrasted with the forces acted by objects outside the system, called external forces A system acted by no external forces is called an isolated system If we consider an isolated system of particles, the only forces involved are pairs of action-reaction forces which cancel each other out two by two. Hence, the net momentum is conserved: p 7 p 1 p 6 p 5 p 2 p 3 p 4 Therefore, in general, for an isolated system of n objects (indexed 1, 2 n) the net momentum, equal to the vector sum of individual momenta is constant: rd by 3 Law nd by 2 Law Fnet Fi Finternal 0 dpnet 0 pnet pi constant i p p p... p m v m v... m v const. 1 2 n n n Note that individual momenta can change, but only such that the sum stays constant i
5 Quiz 1: Momentum and Newton s 2 nd Law: A kid catches a tennis ball and then a basketball, both moving with the same momentum. The kid applies the same force on each ball until it stops. Which of the two balls travels a longer time until it stops? a) Both balls require the same stopping time b) The tennis ball c) The basketball Exercise 1: Conservation of momentum: A man of mass m = 80 kg is initially at rest on a raft of mass M = 150 kg immobile with respect to the still water. Suddenly, the man starts to move to the right with a speed v = 0.50 m/s with respect to the water. Neglect water resistance. a) Write the momenta of the system before and after the man starts walking. b) Calculate the velocity of the raft relative to the water after the man starts walking. m v M
6 Impulse Definition. Impulse-Momentum Theorem The overall effect of applying a force F for a certain time interval Δt can be integrated into a vector physical quantity called impulse a vector denoted J given by the product between a force and the interval of time it acts: 1. If the force F is constant during Δt, the impulse is simply given by 2. If the force is not constant and depend on time as given by a function F(t), the impulse can be obtained analytically by integration: 3. If the force F is not constant during Δt, the impulse can also be found graphically in terms of the average force F av : we see that the impulse is the area under the F vs t curve J F t Force Combining the definition of impulse with Newton s 2 nd Law, we find a way to estimate the average force during motion changing events using: Impulse-Momentum Theorem: The impulse of the average net force acting on a particle for an interval of time is equal to the change in particle s momentum: J av J p Favt t t t 0 F t dt p F av 0 J Ft Δt actual force impulse = area Time
7 Impulse Examples Notice that the Impulse-Momentum Theorem tells us that the same change in momentum can be obtained either by applying a large force a short time interval, or a small force a long time Ex: 1. Instinctual knee protection: when we land after a jump, the change in momentum and consequently the impulse is the same, no matter how long it takes to stop. However, by bending out knees we increase the stopping time which results in a decreased average force onto the knees 2. Car crash air bag protection: The average force suffered by the body during a car crash can be decreased by increasing the time the body changes its momentum from its value before the impact to zero. This is the job of air bags which first inflate extremely fast and then deflate in a controlled time. 3. The table cloth trick: The force (friction) between the objects on a table and the table cloth is constant. However, pulling the cloth away really fast minimizes the impulse, so the change of momentum is small and the objects barely move
8 Exercise 2: Average Force on a Tennis Ball A tennis ball of mass m = 57 g hits a vertical wall with a horizontal speed v = 60 m/s. The collision is filmed with a high speed camera and a profile of the force exerted by the ball onto the wall is plotted versus time. Use the graph to calculate the average force exerted by the wall onto the ball during the collision. Assume the collision elastic. a) What is the collision time interval? Force b) What is the change of momentum during the collision? (Assume the right direction positive.) 0 Δt t (ms) c) Use the Impulse-Momentum Theorem to estimate the average force.
9 Problem: 1. Using the impulse: A rubber ball of mass m = 2.5 kg is dropped from a height y 0 on the floor and bounces back. The graph shows the time evolution of the force of the floor on the ball. a) What is impulse of the ball as it hits the floor? b) What is average force exerted by the floor on the ball? c) How high does the ball bounce?
10 Exercise 3: How Neo should ve listened to the Architect Bad Physics has extenuating circumstances in the movie Matrix, since its world is mostly virtual. However, the movie still perpetuates some misconceptions contradicting elementary Physics even within the logic of its computer controlled reality where people die if their matrix persona dies. For instance, Neo (the local Messiah) saves his lover (vinyl clad Trinity) from death as she falls from a tall building, by catching her hastily right before she hits the sidewalk. Let s compare the average forces acting on Trinity with and without Neo s grab. Assume that Trinity s mass m = 60 kg is about to hit the ground with a speed v i = 50 m/s when Neo arrives and imparts her a very underestimated speed v f = 100 m/s. a) If Neo needs 0.05 s to deflect her fall, what is the average force experienced by Trinity? b) If otherwise Trinity needs 0.05 s to stop when she hits the ground, what is the average force she experiences?
11 Collisions Classification The particles in an isolated system are allowed to interact with each other, so the individual momenta can change. At all times the net momentum must be conserved: p p p p p p p p before after 1 2 n before 1 2 This property is instrumental in handling collisions since the momentum is always conserved during a collision. However, depending on the character of the energy conservation collisions can be: 1. Inelastic, if the objects deform irreversibly during the collision, kinetic energy is not conserved. Yet the momentum is conserved In 1D: p p m v m v m v m v before after If the objects stick together, the collision is called perfectly inelastic and p p m v m v m m v before after velocity of the composite object 2. Elastic, if the objects regain shape after the deformation during the collision the kinetic energy is conserved, as well as the momentum In 1D: p p m v m v m v m v before after During collisions, objects exert forces upon each other. The average force exerted on each colliding object is F av n after mv mv t
12 Exercise 4: Mike s Perfectly Inelastic Collision In the film Back to the future, Michael J. Fox plays the role of a teenager who travels in time, back into the wild-west past of his hometown. Among other adventures, he is challenged to a shootout by wicked Mad Dog Tannen. Mike gets shot, but he s smartly bulletproofed with a stove door. However, the impact with the bullet throws him violently flat on his back. Let s take a look at the scene, and then check out if time traveling is the only dereliction from known Physics in the movie. Estimate realistically the mass of the bullet to be m = 5 g, moving with a speed v bullet = 500 m/s at impact. Also, assume Mike s mass M = 60 kg. a) Considering the impact perfectly inelastic, find Mike s speed right after the impact: b) If the bullet needs 10 ms to stop in the stove door, what is the average force exerted on Mike?
13 Collisions Elastic collisions An application of the concept of kinetic energy is in elastic collisions where both momentum and kinetic energy are conserved since the net work done by the forces exerted by the colliding objects upon each other is overall zero Only for head-on elastic collisions, the conservation of kinetic energy can be reduced to a simpler form: before m 1 collision W net = 0 v1 v 2 m 2 m v v m v m v m v v v v after v v 2 1 Problems: 3. Equations for head-on elastic collision: Demonstrate that the conservation of momentum and kinetic energy in elastic collisions leads to the equations above. 4. Head-on elastic collision with stationary target: Two objects of masses m 1 and m 2 collide head-on. Mass m 1 has an initial speed v 1, and mass m 2 is initially at rest. a) Calculate the speeds of the masses after collision in terms of the given quantities. b) Comment on what is going to happen if m 1 = m 2, and if one the objects is much more massive than the other
14 Problem: 5. Inelastic collision: A bullet of mass m 1 = 5.00 g is fired with a horizontal speed v 1 into a wooden block of mass m 2 = 1.0 kg moving on a horizontal surface with speed v 2 = 2.0 m/s. The coefficient of kinetic friction between the block and surface is μ k = The bullet remains embedded in the block, which is observed to slide a distance d = 0.25 m in the opposite direction than its initial motion before stopping. a) What was the initial speed v 1 of the bullet? b) What is the force exerted by the bullet on the block during the collision, if it took a time Δt = 10 ms to change its direction of motion? m 1 v 1 m 2 v 2 v = 0 μ k d
15 Collisions Multidimensional conservation of momentum The conservation of momentum during collisions is a vector relationship p p p p p p p p before after 1 2 n before 1 2 So, the relationship can be applied to the components of the net momentum, resulting in a number of independent equations corresponding to the dimensionality of the collision: p p p, p, p i x y z p p p... p m v m v... m v const. x 1x 2x nx 1 1x 2 2 x n nx p p p... p m v m v... m v const. y 1y 2 y ny 1 1y 2 2 y n ny p p p... p m v m v... m v const. z 1z 2z nz 1 1z 2 2z n nz n 1D after 2D 3D Ex: If a billiard ball collides with another ball initially at rest, the 2D conservation of momentum can be written: p p before p 1 2 pafter p p p p 1 p 2 p p p 1x 1x 2x 1y 1y 2 y p 1 p 1 p 2
16 Problem: 6. Two dimensional collision: Ball (2) rests on a flat surface when it is struck by a second identical ball (1), which was originally traveling at v 1 = 40.0 m/s. Ball 1 is deflected an angle α = 30 from its original direction. Also, as a result of the collision, ball 2 starts moving at an angle θ = 45 with respect to the original direction of ball 1. a) Draw a vector diagram with the momenta of the balls before and after the collision b) Write the conservation of momentum in a suitable system of coordinates c) Calculate the speeds of each ball after collision 1 1 v 1 v 1 α θ 2 v 2
Chapter 6 Momentum and Collisions
Chapter 6 Momentum and Collisions Momentum and Its Relation to Force Impulse Conservation of Momentum Collisions Classification Inelastic Collisions in One Dimension Elastic Collisions in One Dimension
More informationChapter 6 Momentum and Collisions
Chapter 6 Momentum and Collisions Momentum and Its Relation to Force Impulse Conservation of Momentum Collisions Classification Inelastic Collisions in One Dimension Elastic Collisions in One Dimension
More information1 kg. 10,000 kg. 1 Page. Momentum is a vector so it has a magnitude and a velocity. Its magnitude is the product of its mass and velocity, p = mv.
Momentum The momentum of a single object is simply equal to the product of its mass and its velocity. The symbol for momentum is p. Since mass is a scalar and velocity is a vector, momentum is also a vector.
More informationChapter 9. 9 Momentum. Momentum. PowerPoint Lectures for College Physics: A Strategic Approach, Second Edition Pearson Education, Inc.
Chapter 9 Momentum PowerPoint Lectures for College Physics: A Strategic Approach, Second Edition 9 Momentum Slide 9-2 Slide 9-3 1 Slide 9-4 Reading Quiz 1. Impulse is A. a force that is applied at a random
More information23. A force in the negative direction of an x-axis is applied for 27ms to a 0.40kg ball initially moving at 14m/s in the positive direction of the
23. A force in the negative direction of an x-axis is applied for 27ms to a 0.40kg ball initially moving at 14m/s in the positive direction of the axis. The force varies in magnitude, and the impulse has
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 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 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 informationChapter 9. Momentum. PowerPoint Lectures for College Physics: A Strategic Approach, Second Edition Pearson Education, Inc.
Chapter 9 Momentum PowerPoint Lectures for College Physics: A Strategic Approach, Second Edition 9 Momentum Slide 9-2 Slide 9-3 Slide 9-4 Reading Quiz 1. Impulse is A. a force that is applied at a random
More informationImpulse (J) J = FΔ t Momentum Δp = mδv Impulse and Momentum j = (F)( p = ( )(v) F)(Δ ) = ( )(Δv)
Impulse (J) We create an unbalancing force to overcome the inertia of the object. the integral of force over time The unbalancing force is made up of the force we need to unbalance the object and the time
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 informationPhysics. Impulse & Momentum
Physics Impulse & Momentum Warm up - Write down everything you know about impulse and momentum. Objectives Students will learn the definitions and equations for impulse, momentum, elastic and inelastic
More informationPHYS 154 Practice Test 3 Spring 2018
The actual test contains 1 multiple choice questions and 2 problems. However, for extra exercise, this practice test includes 4 problems. Questions: N.B. Make sure that you justify your answers explicitly
More informationAP Physics 1 Momentum and Impulse Practice Test Name
AP Physics 1 Momentum and Impulse Practice Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A rubber ball and a lump of clay have equal
More informationUNIT 2G. Momentum & It s Conservation
Name: Date:_ UNIT 2G Momentum & It s Conservation Momentum & Newton s 2 nd Law of Motion Newton s 2 nd Law states When an unbalanced force acts upon a body, it accelerates that body in the direction of
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 and Its Relation to Force
Linear Momentum Momentum and Its Relation to Force Momentum is a vector symbolized by the symbol p, and is defined as: It is a vector and has units of: (kg m/s) or (Ns) The rate of change of momentum is
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 informationName: Class: Date: p 1 = p 2. Given m = 0.15 kg v i = 5.0 m/s v f = 3.0 m/s Solution
Assessment Chapter Test A Teacher Notes and Answers Momentum and Collisions CHAPTER TEST A (GENERAL) 1. c 2. c 3. b 4. c 5. a p i = 4.0 kg m/s p f = 4.0 kg m/s p = p f p i = ( 4.0 kg m/s) 4.0 kg m/s =
More informationImpulse simply refers to a change in momentum, and is usually caused by a change in velocity, as described by p = m v.
1 Impulse and Momentum Recall from Newton s 1 st Law: inertia is the tendency of an object to keep on doing what its already doing, that is: either remaining stationary, or: travelling at a constant velocity.
More informationPhysics 100. Today. Finish Chapter 5: Newton s 3 rd Law. Chapter 6: Momentum
Physics 100 Today Finish Chapter 5: Newton s 3 rd Law Chapter 6: Momentum Momentum = inertia in motion Specifically, momentum = mass x velocity = m v Eg. Just as a truck and a roller skate have different
More informationPhysics 100. Today. Finish Chapter 5: Newton s 3 rd Law. Chapter 6: Momentum
Physics 100 Today Finish Chapter 5: Newton s 3 rd Law Chapter 6: Momentum Momentum = inertia in motion Specifically, momentum = mass x velocity = m v Eg. Just as a truck and a roller skate have different
More informationThis Week. 7/29/2010 Physics 214 Fall
This Week Momentum Is momentum in basketball physics? Rockets and guns How do spaceships work? Collisions of objects They get impulses! Practical Propulsion 7/29/2010 Physics 214 Fall 2010 1 Momentum What
More informationMomentum and Impulse Practice Multiple Choice
Choose the alternative that best answers the question and record your answer on the Scantron sheet provided 1. A ball of putty is thrown at a wall and sticks to its surface. Which of the following quantities
More informationThis Week. 9/5/2018 Physics 214 Fall
This Week Momentum Is momentum in basketball physics? Rockets and guns How do spaceships work? Collisions of objects They get impulses! Practical Propulsion 9/5/2018 Physics 214 Fall 2018 1 Momentum What
More information3. How long must a 100 N net force act to produce a change in momentum of 200 kg m/s? (A) 0.25 s (B) 0.50 s (C) 1.0 s (D) 2.0 s (E) 4.
AP Physics Multiple Choice Practice Momentum and Impulse 1. A car of mass m, traveling at speed v, stops in time t when maximum braking force is applied. Assuming the braking force is independent of mass,
More informationPSI AP Physics I Momentum
PSI AP Physics I Momentum Multiple-Choice questions 1. A truck moves along a frictionless level road at a constant speed. The truck is open on top. A large load of gravel is suddenly dumped into the truck.
More informationCollisions. Conservation of Momentum Elastic and inelastic collisions. Serway For practice: Chapter 9, problems 10, 11, 23, 70, 75
Collisions Conservation of Momentum Elastic and inelastic collisions Serway 9.3-9.4 For practice: Chapter 9, problems 10, 11, 23, 70, 75 Momentum: p = mv Impulse (a vector) is defined as F t (for a constant
More informationName: Class: Date: d. none of the above
Name: Class: Date: H Phys quiz Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following is the cause of an acceleration? a. speed b. inertia
More information(D) Based on Ft = m v, doubling the mass would require twice the time for same momentum change
1. A car of mass m, traveling at speed v, stops in time t when maximum braking force is applied. Assuming the braking force is independent of mass, what time would be required to stop a car of mass m traveling
More informationSometimes (like on AP test) you will see the equation like this:
Work, Energy & Momentum Notes Chapter 5 & 6 The two types of energy we will be working with in this unit are: (K in book KE): Energy associated with of an object. (U in book PE): Energy associated with
More informationPhys101 Lectures 14, 15, 16 Momentum and Collisions
Phys101 Lectures 14, 15, 16 Momentum and Collisions Key points: Momentum and impulse Condition for conservation of momentum and why How to solve collision problems Centre of mass Ref: 9-1,2,3,4,5,6,7,8,9.
More informationMomentum and Impulse
Momentum and Impulse Momentum All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. The amount of momentum which an object has is dependent upon two variables:
More informationparticle p = m v F ext = d P = M d v cm dt
Lecture 11: Momentum and Collisions; Introduction to Rotation 1 REVIEW: (Chapter 8) LINEAR MOMENTUM and COLLISIONS The first new physical quantity introduced in Chapter 8 is Linear Momentum Linear Momentum
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 information5.1 Momentum and Impulse
Figure 1 When you hit a ball with a bat, the resulting collision has an effect on both the ball and the bat. linear momentum (p > ) a quantity that describes the motion of an object travelling in a straight
More informationSlide 1 / 40. Multiple Choice AP Physics 1 Momentum
Slide 1 / 40 Multiple Choice AP Physics 1 Momentum Slide 2 / 40 1 A truck moves along a frictionless level road at a constant speed. The truck is open on top. A large load of gravel is suddenly dumped
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 informationMomentum in 1-Dimension
Momentum in 1-Dimension Level : Physics I Date : Warm-up Questions If you were in a car that was out of control and had to choose between hitting a concrete wall or a haystack to stop, which would you
More informationChapter 9 Impulse and Momentum
Chapter 9 Impulse and Momentum Chapter Goal: To understand and apply the new concepts of impulse and momentum. Slide 9-2 Chapter 9 Preview Slide 9-3 Chapter 9 Preview Slide 9-4 Chapter 9 Preview Slide
More information7.1 Momentum. Can you have inertia sitting in your seat? Do you have momentum (relative to the room) sitting in your seat? What is momentum?
Impulse & Momentum 7.1 Momentum Can you have inertia sitting in your seat? Do you have momentum (relative to the room) sitting in your seat? What is momentum? 2 7.1 Momentum Which is harder to stop a truck
More informationCh 6 Homework. Name: Homework problems are from the Serway & Vuille 10 th edition. Follow the instructions and show your work clearly.
Ch 6 Homework Name: Homework problems are from the Serway & Vuille 10 th edition. Follow the instructions and show your work clearly. 1. (Conceptual questions 6.) A skater is standing still on a frictionless
More informationHONORS PHYSICS Linear Momentum
HONORS PHYSICS Linear Momentum LESSON OBJECTIVES Students will be able to... understand that forces can act over time (impulse) resulting in changes in momentum identify characteristics of motion with
More informationAP Physics 1 Momentum
Slide 1 / 133 Slide 2 / 133 AP Physics 1 Momentum 2015-12-02 www.njctl.org Slide 3 / 133 Table of Contents Click on the topic to go to that section Momentum Impulse-Momentum Equation The Momentum of a
More informationToday's goal: I can explain and apply concepts of work and energy (3U) to real world applicaons.
Lesson21.notebook September 17, 2013 Work and Energy A 3U Review Today's goal: I can explain and apply concepts of work and energy (3U) to real world applicaons. What is Work? How do we calculate it? Example:
More informationPer 3 4 Momentum_Presentation.notebook. January 23, 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 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 informationPart I Review Unit Review Name Momentum and Impulse
Part I Review Unit Review Name Momentum and Impulse 1. A 5.00-kilogram block slides along a horizontal, frictionless surface at 10.0 meters per second for 4.00 seconds. The magnitude of the block's momentum
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 informationPhysics 111: Mechanics Lecture 8
Physics 111: Mechanics Lecture 8 Bin Chen NJIT Physics Department Chapter 8 Momentum, Impulse, and Collisions q q q q q q 8.1 Momentum and Impulse 8.2 Conservation of Momentum 8.3 Momentum Conservation
More informationUnit 8. Unit 8 - MTM. Outcomes. Momentum. Solve this problem. What does the word momentum mean to you?
Outcomes Unit 8 THE MOMENTUM TRANSFER MODEL (MTM) I M P U L S E A N D M O M E N T U M What does the word momentum mean to you? Unit 8 - MTM P A R T 1 F O R C E S C H A N G E M O M E N T U M The home team
More informationMechanics. Time (s) Distance (m) Velocity (m/s) Acceleration (m/s 2 ) = + displacement/time.
Mechanics Symbols: Equations: Kinematics The Study of Motion s = distance or displacement v = final speed or velocity u = initial speed or velocity a = average acceleration s u+ v v v u v= also v= a =
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 informationConservation of Momentum
Conservation of Momentum Newton: Quantity of Motion Forces applied for a period of time change an object s quantity of motion. F = ma F = m Δ v t F t = mδv = mv f mv i p mv Ft = Δp F = dp dt Conservation?
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 informationUnit 8. Unit 8 - MTM. Outcomes. What does the word momentum mean to you?
Outcomes Unit 8 THE MOMENTUM TRANSFER MODEL (MTM) I M P U L S E A N D M O M E N T U M Unit 8 - MTM P A R T 1 F O R C E S C H A N G E M O M E N T U M P A R T 2 M O M E N T U M I S C O N S E R V E D What
More informationMomentum is a property of moving matter. Momentum describes the tendency of objects to keep going in the same direction with the same speed.
Warm-up A mosquito collides head-on with a car traveling 60 mph. How do you think the size of the force that car exerts on the mosquito compares to the size of the force that mosquito exerts on car? 12.1
More informationPhysics 231 Lecture 14
Physics 231 Lecture 14 Impulses: forces that last a short time Momentum: p = mv Impulse-Momentum theorem: FΔt = Δp = mδv = m( v f v i ) Momentum conservation: p tot,f p 1,f + p 2,f = p 1,i + p 2,i p tot,i
More information1/9/2017. Newton s 2 nd Law of Motion, revisited
Discuss the forces involved (relative size, direction, name of, etc.) in each of the following scenarios: Coasting to a stop at a stop sign Crashing into wall during a car race Accelerating to the speed
More informationAP Physics Momentum Practice Test. Answers: A,E,E,A,E,B,D,C,B,A,B,E,D,C 16.(a)5450,5650 (b)2.25e7 (c)3 (d)1.5e7 17.(a)9 (b)2 (c)1.5 (d) (e).
AP Physics Momentum Practice Test Answers: A,E,E,A,E,B,D,C,B,A,B,E,D,C 16.(a)5450,5650 (b).5e7 (c)3 (d)1.5e7 17.(a)9 (b) (c)1.5 (d)-4.75 (e).65 For multiple choice ( points) write the CAPITAL letter of
More informationThe graph shows how an external force applied to an object of mass 2.0 kg varies with time. The object is initially at rest.
T2-2 [195 marks] 1. The graph shows how an external force applied to an object of mass 2.0 kg varies with time. The object is initially at rest. What is the speed of the object after 0.60 s? A. 7.0 ms
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 information1. A tennis ball of mass m moving horizontally with speed u strikes a vertical tennis racket. The ball bounces back with a horizontal speed v.
1. A tennis ball of mass m moving horizontally with speed u strikes a vertical tennis racket. The ball bounces back with a horizontal speed v. The magnitude of the change in momentum of the ball is A.
More informationChapter 5 Work and Energy
Chapter 5 Work and Energy Work and Kinetic Energy Work W in 1D Motion: by a Constant orce by a Varying orce Kinetic Energy, KE: the Work-Energy Theorem Mechanical Energy E and Its Conservation Potential
More informationPH105 Exam 1 Solution
PH105 Exam 1 Solution 1. The graph in the figure shows the position of an object as a function of time. The letters A-E represent particular moments of time. At which moment shown (A, B, etc.) is the speed
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 informationMomentum. Inertia in Motion
Momentum Inertia in Motion Inertia in Motion Momentum The product of the mass of an object and its velocity Momentum = mass * velocity p = m*v Large momentums can be the result of Large mass: ship, train
More information1. The diagram below shows the variation with time t of the velocity v of an object.
1. The diagram below shows the variation with time t of the velocity v of an object. The area between the line of the graph and the time-axis represents A. the average velocity of the object. B. the displacement
More informationA. Incorrect! Remember that momentum depends on both mass and velocity. B. Incorrect! Remember that momentum depends on both mass and velocity.
AP Physics - Problem Drill 08: Momentum and Collisions No. 1 of 10 1. A car and motor bike are travelling down the road? Which of these is a correct statement? (A) The car will have a higher momentum.
More information6.1 Momentum and Impulse A. What is momentum? Newton defined momentum as the quantity of motion
AP Physics Mechanics Chapter 6 Momentum and Collisions Text chapter 6 - Reading pp. 141-161 - textbook HW -- #1,3,4,6,9,15,16,20,21,23,26,27,25,34,63,70,71 1 6.1 Momentum and Impulse A. What is momentum?
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 17: Ch.15, Sec.2 4
1 / 38 CEE 271: Applied Mechanics II, Dynamics Lecture 17: Ch.15, Sec.2 4 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Tuesday, October 16, 2012 2 / 38 PRINCIPLE
More informationWelcome back to Physics 211
Welcome back to Physics 211 Today s agenda: Impulse and momentum 09-2 1 Current assignments Reading: Chapter 10 in textbook Prelecture due next Tuesday HW#8 due this Friday at 5 pm. 09-2 2 9-2.1 A crash
More informationThink-Pair-Share. Linear Momentum (Ch 9) Linear Momentum, cont. Newton and Momentum
Linear Momentum (Ch 9) The linear momentum of a particle or an object that can be modeled as a particle of mass m moving with a velocity v is defined to be the product of the mass and velocity: p = m v
More informationScience 20 Physics Review
Science 20 Physics Review Name 1. Which velocity-time graph below best represents the motion of an object sliding down a frictionless slope? a. b. c. d. Numerical response 1 The roadrunner is moving at
More informationMomentum Practice Test
Momentum Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following equations can be used to directly calculate an object s momentum,
More informationm/s m/s m/s m/s
P and J review Name 10-FEB-03 1. The diagram shows two carts on a horizontal, frictionless surface being pushed apart when a compressed spring attached to one of the carts is released. Cart A has a mass
More information(A) 0 (B) mv (C) 2mv (D) 2mv sin θ (E) 2mv cos θ
Physics 1 Lesson 8 Forces and Momentum Homework Outcomes 1. Define linear momentum. 2. Determine the total linear momentum of a system. 3. Apply the Law of Conservation of Momentum to solve problems. 4.
More informationMomentum is conserved for all collisions as long as external forces don t interfere.
Momentum is conserved for all collisions as long as external forces don t interfere. Objectives: Identify the factors that affect an object s momentum Identify the factors that affect how much an object
More informationCHAPTER 9 LINEAR MOMENTUM AND COLLISION
CHAPTER 9 LINEAR MOMENTUM AND COLLISION Couse Outline : Linear momentum and its conservation Impulse and Momentum Collisions in one dimension Collisions in two dimension The center of mass (CM) 9.1 Linear
More informationVersion PREVIEW Semester 1 Review Slade (22222) 1
Version PREVIEW Semester 1 Review Slade () 1 This print-out should have 48 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Holt SF 0Rev 10A
More informationChapter 1 about science 1. Differentiate between hypothesis and theory.
Physics A Exam Review Name Hr PHYSICS SCIENTIFIC METHOD FACT HYPOTHESIS LAW THEORY PHYSICAL SCIENCE UNITS VECTOR MAGNITUDE FORCE MECHANICAL EQUILIBRIUM NET FORCE SCALAR RESULTANT TENSION SUPPORT FORCE
More informationCh 7, Momentum and Collisions Definition of impulse Definition of momentum Impulse-Momentum Theorem
Today Ch 7, Momentum and Collisions Definition of impulse Definition of momentum Impulse-Momentum Theorem System of particles Conservation of Momentum 1 Data : Fatality of a driver in head-on collision
More informationPhysics Midterm Review KEY
Name: Date: 1. Which quantities are scalar? A. speed and work B. velocity and force C. distance and acceleration D. momentum and power 2. A 160.-kilogram space vehicle is traveling along a straight line
More informationChapter 4: Dynamics. Newton s Laws
Chapter 4: Dynamics Newton s Laws What if we all jumped at once? Newton s 1st Law Objects with mass have Inertia: the tendency to stay at rest (or moving!) The more mass an object has, the more difficult
More informationChapter 7. Impulse and Momentum
Chapter 7 Impulse and Momentum 1) Linear momentum p = mv (units: kg m / s) 2) Impulse (produces a finite change in momentum) (a) Constant force: J = FΔt From the 2nd law, F = Δ(m v) Δt = Δ p Δt, so J =
More informationPhysics 211: Lecture 14. Today s Agenda
Physics 211: Lecture 14 Today s Agenda Systems of Particles Center of mass Linear Momentum Example problems Momentum Conservation Inelastic collisions in one dimension Ballistic pendulum Physics 211: Lecture
More informationPhysics 11. Unit 5 Momentum and Impulse
Physics 11 Unit 5 Momentum and Impulse 1 1. Momentum It is always amazing to see karate experts chopping woods or blocks. They look so extraordinary and powerful! How could they do that? 2 Let s consider
More informationWallace Hall Academy
Wallace Hall Academy CfE Higher Physics Unit 1 - Dynamics Notes Name 1 Equations of Motion Vectors and Scalars (Revision of National 5) It is possible to split up quantities in physics into two distinct
More informationLINEAR MOMENTUM. Momentum Impulse Conservation of Momentum Inelastic Collisions Elastic Collisions Momentum In 2 Dimensions Center of Mass
LINEAR MOMENTUM Momentum Impulse Conservation of Momentum Inelastic Collisions Elastic Collisions Momentum In 2 Dimensions Center of Mass MOMENTUM Quantity of Motion Product of Mass and Velocity p = mv
More informationWhat physical quantity is conserved during the above inelastic collision between Katy and Aroha? State any assumptions you have made.
MECHANICS: NEWTONS LAWS, MOMENTUM AND ENERGY QUESTIONS ROLLER SKATING (2017;1) Katy, 65.0 kg, and Aroha, 50.0 kg, are roller skating. Aroha is moving to the right at a constant velocity of 6.0 m s 1 and
More informationAP Physics C. Momentum. Free Response Problems
AP Physics C Momentum Free Response Problems 1. A bullet of mass m moves at a velocity v 0 and collides with a stationary block of mass M and length L. The bullet emerges from the block with a velocity
More informationPhysics: Impulse / Momentum Problem Set
Physics: Impulse / Momentum Problem Set A> Conceptual Questions 1) Explain two ways a heavy truck and a person on a skateboard can have the same momentum. 2) In stopping an object, how does the time of
More informationΣp before ± I = Σp after
Transfer of Momentum The Law of Conservation of Momentum Momentum can be transferred when objects collide. The objects exert equal and opposite forces on each other, causing both objects to change velocity.
More informationChapter 9. Linear Momentum and Collisions
Chapter 9 Linear Momentum and Collisions Momentum Analysis Models Force and acceleration are related by Newton s second law. When force and acceleration vary by time, the situation can be very complicated.
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The motion of a particle is described in the velocity versus time graph shown in the
More informationPage 1. Name: Section This assignment is due at the first class in 2019 Part I Show all work!
Name: Section This assignment is due at the first class in 2019 Part I Show all work! 7164-1 - Page 1 1) A car travels at constant speed around a section of horizontal, circular track. On the diagram provided
More informationCircle correct course: PHYS 1P21 or PHYS 1P91 BROCK UNIVERSITY
Tutorial #: Circle correct course: PHYS 1P21 or PHYS 1P91 Name: Student #: BROCK UNIVERSITY Test 7: November 2015 Number of pages: 5 Course: PHYS 1P21/1P91 Number of students: 218 Examination date: 17
More informationm/s m/s m/s m/s
P And J Review TEACHER ANSWER KEY February 10, 2003 2 1. The diagram shows two carts on a horizontal, frictionless surface being pushed apart when a compressed spring attached to one of the carts is released.
More informationIMPACT (Section 15.4)
IMPACT (Section 15.4) Today s Objectives: Students will be able to: a) Understand and analyze the mechanics of impact. b) Analyze the motion of bodies undergoing a collision, in both central and oblique
More informationWhen particle with mass m moves with velocity v, we define its Linear Momentum p as product of its mass m and its velocity v:
8. LINEAR MOMENTUM. Key words: Linear Momentum, Law of Conservation of Momentum, Collisions, Elastic Collisions, Inelastic Collisions, Completely Inelastic Collision, Impulse, Impulse Momentum Theorem.
More information