Introduction to Modern Physics PHYX 2710

Introduction to Modern Physics PHYX 2710

Physics of Technology PHYS 1800 Lecture 15 Introduction Section 0 Momentum Lecture 1 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 1 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet Date Day Lecture Chapter

Jan 5 M Class Admin: Intro.Physics Phenomena 1 6 T Problem solving and math App. B, C 7 W Units, Scalars, Vectors, 1 9 F* Speed and Velocity 2 Jan 12 M Acceleration 2 14 W Free Falling Objects 3 16 F* Projectile Motion 3 Jan 19 M Martin Luther King No Class

21 W Newtons Laws 4 23 F* Mass and Weight 4 Jan 26 M Motion with Friction 4 28 W Review 1-4 1-4 29 Th Test 1 30 F Circular Motion 5 Feb 2 M Planetary Motion and Gravity 5 4 W Energy 6 6

F* Harmonic Motion 6 Feb 9 M Momentum 7 11 W Impulse and Collisions 7 13 F* Rotational Motion 8 Section 0 Lecture 1 Slide 2 Feb 16 Introduction M Presidents Day No Class 17 Tu Angular Momentum (Virtual Monday) 8 18 W Review 5-8 19 5-8 H Test 2 INTRODUCTION

TO Modern Physics PHYX 2710 20 F* Static Fluids, Pressure 9 Feb 23 M Flotation 9 Fall 2004 *Homework 25 WHandout Fluids in Motion 9 27 F* Temperature and Heat 10 Mar 2 M First Law of Thermodynamics 10 Physics of TechnologyPHYS 1800 4 W Heat flow and Greenhouse Effect 10 Momentum

6 F* Climate Change - Homework Due 1 2 3 4 5 6 7 Lecture 15 Slide 2 Physics of Technology PHYS 1800 Lecture 15 Momentum Introduction Section 0 Slide 3 Introduction Lecture 1

INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 3 Describing Motion and Interactions Positionwhere you are in space (L or meter) Velocityhow fast position is changing with time (LT-1 or m/s) Accelerationhow fast velocity is changing with time (LT-2 or m/s2) Force what is required to change to motion of a body (MLT-2 or kg-m/s2 or N) Energythe potential for an object to do work. (ML2T-2 or kg m2/s2 or N-m or J) Work is equal to the force applied times the distance moved. W = F d Kinetic Energy is the energy associated with an objects motion. KE= mv2 Potenital Energy is the energy associated with an objects position. Gravitational potential energy PEgravity=mgh Spring potential energy PEapring= -kx Section 0 Lecture 1 Slide 4 In this chapterIntroduction we will develop the concept ofMOMENTUMand and its associated law of Conservation of Momentum and apply this to collisions. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 4

Momentum and Collisions How can we describe the change in velocities of colliding football players, or balls colliding with bats? How does a strong force applied for a very short time affect the motion? Can we apply Newtons Laws to collisions? What exactly is momentum? How is it different from force or energy? What does Conservation of Momentum mean? Initial time t=tfinal tinitial Introduction Section 0 Lecture 1 INTRODUCTION TO Modern Physics PHYX 2710 W=F d Slide 5 with d=dfinal dinitial Fall 2004 Final time p=F t

Physics of TechnologyPHYS 1800 Momentum with t=tfinal tinitial Lecture 15 Slide 5 A Closer Look at Collisions Look here carefully! Introduction Section 0 Lecture 1 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 6 Compression on an Atomic Scale Bonds between atoms in a compressed solid can be treated as compressed springs.

+ + + + Ultimately the forces come from electrostatic interactions between electrons and protons (and a little quantum mechanics). + + Section 0 + Lecture 1 Slide 7 + + Introduction Fspring=-k x INTRODUCTION TO Modern Physics PHYX 2710

Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 7 What Happens During the Collision? Does Newtons third law still hold? For every action, there is an equal but opposite reaction. The defensive back exerts a force on the fullback, and the fullback exerts an equal but opposite force on the defensive back. Introduction Section 0 Lecture 1 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum

Lecture 15 Slide 8 Conservation of Momentum Does Newtons third law still hold? For every action, there is an equal but opposite reaction. The defensive back exerts a force on the fullback, and the fullback exerts an equal but opposite force on the defensive back. Introduction Section 0 Lecture 1 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 9 Conservation of Momentum The impulses on both are equal and opposite.

The changes in magnitude for each are equal and opposite. The total change of the momentum for the two players is zero. Introduction Section 0 Lecture 1 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 10 Conservation of Momentum If the net external force acting on a system of objects is zero, the total momentum of the system is conserved. Introduction

Section 0 Lecture 1 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 11 A 100-kg fullback moving straight downfield collides with a 75-kg defensive back. The defensive back hangs on to the fullback, and the two players move together after the collision. What is the initial momentum of each player? Introduction Section 0 Lecture 1 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800

Momentum Lecture 15 Slide 12 What is the initial momentum of each player? Fullback: p = mv = (100 kg)(5 m/s) = 500 kgm/s2 Introduction Section 0 Lecture 1 Defensive back: p = mv = (75 kg)(-4 m/s) = -300 kgm/s2 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 13

What is the total momentum of the system? Total momentum: ptotal = pfullback + pdefensive back = 500 kgm/s - 300 kgm/s = 200 kgm/s Introduction Section 0 Lecture 1 Slide 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 14 What is the velocity of the two players immediately after the collision? Total mass: m = 100 kg + 75 kg = 175 kg Velocity of both:

v = ptotal / m = (200 kgm/s) / 175 kg = 1.14 m/s Introduction Section 0 Lecture 1 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 15 Recoil Why does a shotgun slam against your shoulder when fired, sometimes painfully? How can a rocket accelerate in empty space when there is nothing there to push against except itself? Introduction Section 0 Lecture 1

Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 16 Two skaters of different masses prepare to push off against one another. Which one will gain the larger velocity? a) The more massive one b) The less massive one c) They will each have equal but opposite velocities. The net external force acting on the system is zero, so conservation of momentum applies. Before the push-off, the total initial momentum is zero. Introduction Section 0 Lecture 1 Slide 17 The total momentum after the push-off should also be zero. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800

Momentum Lecture 15 Slide 17 How can the total momentum be zero when at least one of the skaters is moving? Both must move with momentum values equal in magnitude but opposite in direction: p2 = p1 When added together, the total final momentum of the system is then zero. Since momentum is mass times velocity p = mv, the Section 0 Lecture skater with Introduction the smaller mass must have the larger velocity: m1v1 = m2v2 1 Slide 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum

Lecture 15 Slide 18 Recoil is what happens when a brief force between two objects causes the objects to move in opposite directions. The lighter object attains the larger velocity to equalize the magnitudes of the momentums of the two objects. The total momentum of the system is conserved and does not change. Introduction Section 0 Lecture 1 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum

Lecture 15 Slide 19 Is momentum conserved when shooting a shotgun? The explosion of the powder causes the shot to move very rapidly forward. If the gun is free to move, it will recoil backward with a momentum equal in magnitude to the momentum of the shot. Introduction Section 0 Lecture 1 Slide 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 20

Even though the mass of the shot is small, its momentum is large due to its large velocity. The shotgun recoils with a momentum equal in magnitude to the momentum of the shot. The recoil velocity of the shotgun will be smaller than the shots velocity because the shotgun has more mass, but it can still be sizeable. Introduction Section 0 Lecture 1 Slide 21 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 21 How can you avoid a bruised shoulder? If the shotgun is held firmly against your shoulder, it doesnt hurt as much. WHY? Introduction

Section 0 Lecture 1 Slide 22 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 22 If you think of the system as just the shotgun and the pellets, then your shoulder applies a strong external force to the system. Since conservation of momentum requires the external force to be zero, the momentum of this system is not conserved. Introduction Section 0 Lecture 1 Slide 23

INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 23 If you think of the system as including yourself with your shoulder against the shotgun, then momentum is conserved because all the forces involved are internal to this system (except possibly friction between your feet and the earth). With your mass added to the system, the recoil velocity is smaller. Introduction Section 0 Lecture 1 Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800

Momentum Lecture 15 Slide 24 If you think of the system as including yourself and the earth, then momentum is conserved because all the forces involved are internal to this system. The large mass of the earth means that the change in momentum of the earth would be imperceptible. Introduction Section 0 Lecture 1 Slide 25 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 25 How does a rocket accelerate in empty space when there is nothing to push against?

The exhaust gases rushing out of the tail of the rocket have both mass and velocity and, therefore, momentum. The momentum gained by the rocket in the forward direction is equal to the momentum of the exhaust gases in the opposite direction. The rocket and the exhaust gases push against each other. Newtons third law applies. Introduction Section 0 Lecture 1 Slide 26 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 26 Elastic and Inelastic Collisions Energy is not conserved in a perfectly inelastic collision. If the objects bounce apart instead of sticking together, the collision is either elastic or partially

inelastic. An elastic collision is one in which no energy is lost. A partially inelastic collision is one in which some energy is lost, but the objects do not stick together. Introduction Section 0 Lecture 1 Slide 27 The greatest portion of energy is lost in the perfectly inelastic collision, when the objects stick. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 27 A ball bouncing off a floor or wall with no decrease in the magnitude of its velocity is an elastic collision. The kinetic energy does not decrease. No energy has been lost. A ball sticking to the wall is a perfectly inelastic collision. The velocity of the ball after the collision is zero. Its kinetic energy is then zero. All of the kinetic energy has been lost. Most collisions involve some energy loss, even if the objects do not stick, because the collisions are not perfectly elastic. Introduction

Section 0 Lecture 1 Slide 28 Heat is generated, the objects may be deformed, and sound waves are created. These would be partially inelastic collisions. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 28 What happens when billiard balls bounce? Simplest case: a head-on collision between the white cue ball and the eleven ball initially at rest. If spin is not a factor, the cue ball stops and the eleven ball moves forward with a velocity equal to the initial velocity of the cue ball. The eleven balls final momentum is equal to the cue balls initial momentum. Momentum is conserved. The eleven ball also has a final kinetic energy equal to the cue balls 0 Lecture 1 Slide 29 initial Introduction

kineticSection energy. Energy is conserved. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 29 What happens when billiard balls bounce? For equal masses, the only way for momentum and energy to both be conserved is for the cue ball to stop and the eleven ball to move forward with all the velocity. Another example is the familiar swinging-ball toy with a row of steel balls hanging by threads from a frame. If one ball is pulled back and released, the collision with the other balls results in a single ball from the other end flying off with the same velocity as the first ball just before the collision. Both momentum and kinetic energy are conserved. If two balls on one side are pulled back and released, two balls fly off from the opposite side. Why doesnt one ball fly off with twice the

velocity? Introduction Section 0 Lecture 1 Slide 30 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 30 Collisions at an Angle Two football players traveling at right angles to one another collide and stick together. What will be their direction of motion after the collision? Introduction Section 0 Lecture 1 Add the individual momentum vectors to get the total momentum of the system before

the collision. The final momentum of the two Slide 31 players stuck together is equal to the total initial momentum. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 31 Collisions at an Angle The total momentum of the two football players prior to the collision is the vector sum of their individual momentums. The larger initial momentum has a larger effect on the final direction of motion. Introduction Section 0 Lecture 1 Slide 32 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004

Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 32 Two lumps of clay of equal mass are traveling at right angles with equal speeds as shown, when they collide and stick together. Is it possible that their final velocity vector is in the direction shown? a) b) c) yes no unable to tell from this graph No. The final momentum will be in a direction making a Introduction Section 0 Lecture 1 Slide 45o degree angle with respect to each of the initial momentum vectors. 33 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of TechnologyPHYS 1800

Momentum Lecture 15 Slide 33 Two cars of equal mass Collide at right angles to one another in an intersection. Their direction of motion after the collision is as shown. Which car had the greater velocity before the collision? a) b) c) d) Car A Car B Their velocities were equal in magnitude. It is impossible to tell from this graph. Since the angle with respect to the original direction of A is Introduction Section 0 Lecture 1 smaller than 45, car A must have had a larger momentum and thus was traveling faster. Slide 34 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004

Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 34 Physics of Technology Next Lab/Demo: Next Class: Introduction Section 0 Lecture 1 Test 2 Thursday 1:30-2:45 ESLC 46 Ch 5 through 8 Tuesday 10:30-11:20 BUS 318 room Slide 35 Review Ch 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004

Physics of TechnologyPHYS 1800 Momentum Lecture 15 Slide 35

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