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Physics of Technology PHYS 1800 Lecture 7 Introduction Newton’s Laws Section 0 Lecture 1 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 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 Newton’s 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 13Introduction F* Rotational 8 Section 0 Motion Lecture 1 Slide 2 Feb 16 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 Fall 2004 Feb 23 M Flotation 9 25 W Fluids in Motion 9 27 F* Temperature and Heat 10 Mar 2 M First Law of Thermodynamics 10 Physics of Technology—PHYS 1800 4 W Spring 2009Heat flow and Greenhouse Effect 10 Newton’s Laws *Homework Handout 6 F* Climate Change - Homework Due - 1 2 3 4 5 - 6 Lecture 7 Slide 2 7 Physics of Technology PHYS 1800 Lecture 6 Newton’s Laws Introduction Section 0 Lecture 1 Slide 3 Introduction and Significance INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 3 Describing Motion Position—where you are in space (L-meter) Speed—how fast position is changing with time (LT-1 or m/s) Acceleration—how fast speed is changing with time (LT-2 or m/s2) Introduction Section 0 Lecture 1 Slide 4 Question: How do we get things to accelerate? INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 4 Acceleration Acceleration is the rate at which velocity changes. – Our bodies don’t feel velocity, if the velocity is constant. – Our bodies feel acceleration. • A car changing speed or direction. • An elevator speeding up or slowing down. Acceleration can be either a change in the object’s speed or direction of motion. Change in velocity V2 - V1 = Average acceleration = t Time interval Introduction Section 0 Lecture 1 Slide 5 r r a = DV m s 2 t In this Chapter acceleration is a variable, caused by FORCE. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 5 Acceleration Due to Gravity • Earth exerts a gravitational force on objects that is attractive (towards Earth’s surface). • Near Earth’s surface, this force produces a constant acceleration downward. – To measure this acceleration, we need to slow down the action. – Galileo was the first to accurately measure this acceleration due to gravity. – By rolling objects down an inclined plane, he slowed the motion enough to establish that the gravitational acceleration uniform, Introduction Section 0is Lecture 1 Slide or 6 constant with time. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 6 How does this trajectory happen? Key: - resolve motion into its HORIZONTAL and VERTICAL components. VH = constant VTOTAL VG (due to gravity) But we know VG increases with time due to gravity acceleration! VH (constant) At any instant the total velocity is vector sum of VH and VG Resultant TRAJECTORY Introduction Section 0 Lecture 1 Slide 7 STEEPENS with increasing time. Uniform increase in VG with time INTRODUCTION TO Modern Physics PHYX 2710 As NO horizontal acceleration the ball moves equal distances horizontally in equal time (assuming NO air resistance). Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 7 One Heck of a Ball Team!!! Hart’s list of most influential people in the history of the world: Newton (2)* Einstein (10) Galileo Galilei (12)* Aristole (13)*** Copernicus (19) * Kepler (75) * *(even though they got the wrong answer on the test) Introduction Section 0 Lecture INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Simmon’s list of most influential scientists in the history of the world Newton (1)* (and 2 and 6 and 40) Einstein (2) 1 Slide 8 Galileo Galilei (7)* Copernicus (9) Kepler (10) Tyco Brahe (22) Aristole (an honorable mentioned)*** Newton’s Laws Lecture 7 Slide 8 Newton’s Contribution • Newton built on Galileo’s work, expanding it. • He developed a comprehensive theory of motion that replaced Aristotle’s ideas. • Newton’s theory is still widely used to explain ordinary motions. Introduction Section 0 Lecture 1 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 9 Aristotle’s View • A force is needed to keep an object moving. • Air rushing around a thrown object continues to push the object forward. Introduction Section 0 Lecture 1 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 10 Galileo’s Contribution • Galileo challenged Aristotle’s ideas that had been widely accepted for many centuries. • He argued that the natural tendency of a moving object is to continue moving. – No force is needed to keep an object moving. Introduction Section 0 Lecture 1 Slide 11 – This goes against what we seem to experience. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 11 Newton’s First and Second Laws Put Galileo's notions of motion on a mathematical footing with calculus Set up the framework to explain motion. How do forces affect the motion of an object? What exactly do we mean by force? Is there a difference between, say, force, energy, momentum, impulse? What do Newton’s first and second laws of motion tell us, and how are they related to one another? Developed the first hints of a concervation law— Newton’s 3rd Law of Motion. Developed the first formulation of a force—the gravitational force. Introduction Section 0 Lecture 1 Slide 12 Made seminal contributions in thermodynamics and optics. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 12 Inconsistencies in Physics cira 1900 Statistical Mechanics • Boltzmann Distribution • Entropy and counting states Electricity & Magnetism • Medium for propagation of light • Obeys Lorentz transformation • • • • Mechanics (Gravity) • Discrete atomic spectra • Radioactive decay Obeys Galilean transformation Introduction Section 0 • Brownian motion Lecture 1 Blackbody radiation Wein’s Law Photoelectric effect Diffraction of x rays Slide 13 • Existence of Atoms! INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 13 Newton’s Law of Universal Gravitation • Newton recognized the similarity between the motion of a projectile on Earth and the orbit of the moon. • If a projectile is fired with enough velocity, it could fall towards Earth but never reach the surface. • The projectile would be in orbit. • Newton’s law of universal gravitation says the gravitational force between two objects is proportional to the mass of each object, and inversely proportional to the square of the distance between the two objects. Introduction • Section 0 Lecture 1 Slide 14 G is the Universal gravitational constant G. Fgravity = INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Gm1m2 r2 Lecture 7 Slide 14 Dennison’s Laws of Motion 1. Stuff happens (or not). 2. The bigger they are the harder they fall. 3. You get what you give. Introduction Section 0 Lecture 1 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 15 Newton’s First Law of Motion An object remains at rest, or in uniform motion in a straight line, unless it is compelled to change by an externally imposedIntroduction force. Section 0 Lecture 1 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 16 Newton’s Second Law of Motion The acceleration of an object is directly proportional to the magnitude of the imposed force and inversely proportional to the mass of the object. The acceleration is the Introduction Section 0 Lecture 1 same direction as that of the imposed force. Slide 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 17 Newton’s Second Law of Motion Note that a force is proportional to an object’s acceleration, not its velocity. Precise definitions of some commonly used terms: The mass of an object is a quantity that tells us how much resistance the object has to a change in its motion. This resistance to a change in motion is called inertia. F = ma Introduction Section 0 Lecture 1 Slide 18 units : 1 newton = 1 N = 1 kg m s2 Force has dimensions of (MLT-2) INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 18 Fstring = 10 N (to the right) Net Forces It is the total force or net force that determines an object’s acceleration. If there is more than one vector acting on an object, the forces are added together as vectors, taking into account their directions. ftable = 2 N (to the left) Fnet = 10 N - 2 N = 8 N (to the right) Fnet 8 N a= = m 5 kg = 1.6 m s2 (to the right) Introduction Section 0 Lecture 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Slide 19 Newton’s Laws Lecture 7 Slide 19 Two equal-magnitude horizontal forces act on a box. Is the object accelerated horizontally? a) b) c) Since the two forces are equal in size, and are in opposite directions, they cancel each other out and there is no acceleration. Yes. No. You can’t tell from this diagram. Introduction Section 0 Lecture 1 Slide 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 20 Is it possible that the box is moving, since the forces are equal in size but opposite in direction? a) a) Yes, it is possible for the object to be moving. No, it is impossible for the object to be moving. Introduction Section 0 Lecture 1 Even though there is no acceleration, it is possible the object is moving at constant speed. Slide 21 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 21 Two equal forces act on an object in the directions shown. If these are the only forces involved, will the object be accelerated? a) b) c) Yes. No. It is impossible to determine from this figure. The vector sumSection of the forces in a Introduction 0 two Lecture 1 Slideresults 22 force directed toward the upper right corner. The object will be accelerated toward the upper right corner. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 22 Two forces act in opposite directions on a box. What is the mass of the box if its acceleration is 4.0 m/s2? a) b) c) d) e) The net force is 50 N - 30 N = 20 N, directed to the right. 5 kg 7.5 kg 12.5 kg 80 kg 120 kg From F=ma, the mass is given by: m = F/a = (20 N) / (4 m/s2) = 5 kg. Introduction Section 0 Lecture 1 Slide 23 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 23 A 4-kg block is acted on by three horizontal forces. What is the net horizontal force acting on the block? a) b) c) d) e) 10 N 20 N 25 N 30 N 40 N The net horizontal force is: 5 N + 25 N - 10 N = 20 N directed to the right. Introduction Section 0 Lecture 1 Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 24 A 4-kg block is acted on by three horizontal forces. What is the horizontal acceleration of the block? From F=ma, the acceleration is given by: a) b) c) d) e) 10 N 20 N 25 N 30 N 40 N a = F/m = (20 N) / (4 kg) = 5 m/s2 directed to the right. Introduction Section 0 Lecture 1 Slide 25 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 25 A ball hangs from a string attached to the ceiling. What is the net force acting on the ball? a) b) c) The net force is downward. The net force is upward. The net force is zero. Since the ball is hanging from the ceiling at rest, it is not accelerating so the net force is Introduction Section 0 Lecture 1 Slide 26 zero. There are two forces acting on the ball: tension from the string and force due to gravitation. They cancel each other. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 26 Two masses connected by a string are placed on a fixed frictionless pulley. If m2 is larger than m1, will the two masses accelerate? a) b) c) Yes. No. You can’t tell from this diagram. Introduction Section Lecture 1 Slide 27 The acceleration of0the two masses will be equal and will cause m2 to fall and m1 to rise. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 27 Newton’s Third Law • Where do forces come from? • If we push on an object like a chair, does the chair also push back on us? • If objects do push back, who experiences the greater push, us or the chair? • Does our answer change if we are pushing against a wall? Introduction Section 0 Lecture 1 Slide 28 • How does Newton’s third law of motion help us to define force, and how is it applied? INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 28 Newton’s Third Law (“action/reaction”) For every action (force), there is an equal but opposite reaction (force). Introduction Section 0 Lecture 1 Slide 29 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 29 Identifying the forces acting on an object. • The forces acting on the book are W (gravitational force from Earth) and N (normal force from table). • Normal force refers to the perpendicular force a surface Introduction Section 0 exerts on an object. Lecture 1 Slide 30 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 30 Third-Law Action/Reaction Pair An uncompressed spring and the same spring supporting a book. The compressed spring exerts an upward force on the book. Introduction Section 0 Lecture 1 Slide 31 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 31 Third-Law Action/Reaction Pair If the cart pulls back on the mule equal and opposite to the mule’s pull on the cart, how does the cart over move? Introduction Section 0 Lecture 1 Slide 32 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 32 Third-Law Action/Reaction Pair The car pushes against the road, and the road, in turn, pushes against the car. Introduction Section 0 Lecture 1 Slide 33 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 33 Newton’s Laws in Review • 2nd Law (and 1st Law)—How motion of a object is aeffected by a force. • 3rd Law—Forces come from interactions with other objects. • Two branches of Mechanics: • • Statics using the 1st Law with a=0 or Fnet=0 Dynamics using the 2nd Law with a≠0 or Fnet ≠0 • Note: At the most fundamental level, there are only 4 forces in nature, gravity, electricity and magnetism, Introduction Section 0 Lecture 1 and Slide strong 34 tweak nuclear force nuclear force. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 34 Dennison’s Laws of Motion 1. Stuff happens (or not). 2. The bigger they are the harder they fall. 3. You get what you give. Introduction Section 0 Lecture 1 Slide 35 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 35 Free Body Diagrams • Fancy Science: Vector analysis of complex force problems is facilitated by use of a free body diagram. • Common Sense: A picture is worth a 100 words. (A scale picture is worth an A!) • Key is to: • Isolate a single body and draw all the forces acting on it. • Add up all the arrows (vectors). Introduction Section 0 Lecture 1 Slide 36 • What’s left is the net force. • Net force (and masses) a. • A plus initial conditions motion! INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 36 Physics of Technology Next Lab/Demo: Forces Thursday 1:30-2:45 ESLC 53 Ch 3 Next Class: Wednesday 10:30-11:20 Slide 37 BUS 318 room Read Ch 4 Introduction Section 0 Lecture 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws Lecture 7 Slide 37