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Transcript
Physics of Technology PHYS 1800 Lecture 8 Introduction Mass & Weight Motion with Friction Section 0 Lecture 1 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 1 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet Date Day Lecture Jan 5 M Class Admin: Intro.Physics Phenomena 6 T Problem solving and math 7 W Units, Scalars, Vectors, 9 F* Speed and Velocity Jan 12 M Acceleration 14 W Free Falling Objects 16 F* Projectile Motion Jan 19 M Martin Luther King 21 W Newton’s Laws 23 F* Mass and Weight Jan 26 M Motion with Friction 28 W Review 29 Th Test 1 30 F Circular Motion Feb 2 M Planetary Motion and Gravity 4 W Energy 6 F* Harmonic Motion Feb 9 M Momentum 11 W Impulse and Collisions 13Introduction F* Rotational Section 0 Motion Lecture 1 Slide 2 Feb 16 M Presidents Day 17 Tu Angular Momentum (Virtual Monday) 18 W Review 19 H Test 2 INTRODUCTION TO Modern Physics PHYX 2710 20 F* Static Fluids, Pressure Fall 2004 Feb 23 M Flotation 25 W Fluids in Motion 27 F* Temperature and Heat Mar 2 M First Law of Thermodynamics Physics of Technology—PHYS 1800 4 W Spring 2009Heat flow and Greenhouse Effect Mass & Weight *Homework Handout 6 F* Climate Change Chapter 1 App. B, C 1 2 2 3 3 No Class 4 4 4 1-4 1-4 5 5 6 6 7 7 8 No Class 8 5-8 5-8 9 9 9 10 10 10Friction - Homework Due - 1 2 3 4 5 - 6 Lecture 8-9 Slide 2 7 Physics of Technology PHYS 1800 Lecture 8 Mass & Weight Motion with Friction Introduction Section 0 Lecture 1 Slide 3 Introduction and Review INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 3 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 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 4 Newton’s Laws in Review • 1st Law —a special case of the 2nd Law for statics, with a=0 or Fnet=0 • An objects velocity remains unchanged, unless a force acts on the object. • 2nd Law (and 1st Law)—How motion of a object is effected by a force. – 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 same direction as that of the imposed force. F ma units : 1 newton = 1 N = 1 kg m s2 • Introduction Section 0 Lecture 1 Slide 5 3rd Law —Forces come from interactions with other objects. • For every action (force), there is an equal but opposite reaction (force). INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 5 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 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 6 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 same direction as that of the imposed force. Introduction Section 0 Lecture 1 Slide 7 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 7 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 8 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 Mass & Weight Friction Lecture 8-9 Slide 8 Physics of Technology PHYS 1800 Lecture 8 Mass & Weight Motion with Friction Introduction Section 0 Lecture 1 Slide 9 Mass & Weight INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 9 Mass and Weight • What exactly is mass? • Is there a difference between mass and weight? • If something is weightless in space, does it still have mass? Introduction Section 0 Lecture 1 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 10 Mass, Weight, and Inertia • A much larger force is required to produce the same acceleration for the larger mass. • Inertia is an object’s resistance to a change in its motion. • Mass is a measure of an object’s inertia. Introduction Section 0 Lecture 1 Slide 11 • The units of mass are kilograms (kg). INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 11 Mass, Weight, and Inertia • An object’s weight is the gravitational force acting on the object. • Weight is a force, measured in units of newtons (N). • In the absence of Section 0 Lecture gravity,Introduction an object has no weight but still has the same mass. 1 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 12 Mass Standard How do we determine what the magnitude of a gravitational force (weight) is? The International Prototype Kilogram (“IPK”) is the kilogram. It sits next to an inchbased ruler for scale. The IPK is made of a platinum-iridium alloy Introduction Section 0 Lecture and is stored in a vault at the BIPM in Sèvres, France. 1 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 13 Mass, Weight, and Inertia • Objects of different mass experience the same gravitational acceleration on Earth: g = 9.8 m/s2 • By Newton’s 2nd Law, F = ma, the weight is W = mg. • Different gravitational forces (weights) act on falling objects Introduction of different Sectionmasses, 0 Lecture 1 Slide but the objects have the same acceleration. 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 14 Weight Example: A body of mass 100 kg on the moon weighs: W = m . g = 100 x 9.8 / 6 = 163 N (Compared with 980 N on Earth) Note: In English (imperial) system, weight (W) is measured in lbs (pounds) – which is also a force. 1 lbs = 4.45 N so, W = 163 N = 36.6 lbs only! Introduction Section 0 Lecture 1 Slide 15 A mass of 1 kg therefore weighs 2.2 lbs near Earth’s surface (or 9.8 N). INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 15 Physics of Technology PHYS 1800 Lecture 8 Mass & Weight Motion with Friction Introduction Section 0 Lecture 1 Slide 16 A closer Look at Forces INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 16 A Closer Look at the Table • 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 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 17 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 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 18 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 19 + + Introduction Fspring=-k Δx + INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 19 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 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 20 What is friction? • A resistive force opposing motion. • So far we have assumed many examples with no friction but friction is a very important force in our lives… • No surface is perfectly smooth when viewed at the atomic level! • Frictional forces arise between two surfaces in contact because they tend to dig into each other. Introduction Section 0 Lecture 1 Slide 21 Two objects in contact supported by a few high spots or “prominences”. INTRODUCTION TO Modern Physics PHYX 2710 contact points Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 21 What is friction? • Friction is known to be independent of surface area – counter intuitive! • Reasoning: If reduce area, the number of contact points reduces. This causes the pressure to increase at these points, which in turn flattens them more and results in an increase in contact area. • Overall effect: total “contact area” about the same! • There are no simple “laws of friction”, as it is affected by several factors, eg: – Surface quality (roughness) – Type of material Introduction Section 0 Lecture 1 Slide 22 – Presence of lubricants… • Lubricants act to separate the two surfaces and allow them to “float” – greatly reducing the friction. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 22 Physics of Technology PHYS 1800 Lecture 8 Mass & Weight Motion with Friction Introduction Section 0 Lecture 1 Slide 23 Introduction and Review INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 23 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 24 • 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 Mass & Weight Friction Lecture 8-9 Slide 24 Does a sky diver continue to accelerate? Air resistance R is a force directed upward, that opposes the gravitational force W R increases as the sky diver’s velocity increases When R has increased to the magnitude of W, the net force is zero so the acceleration is zero Introduction Section 0 Lecture 1 Slide 25 The velocity is then at its maximum value, the terminal velocity INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 25 Example: Sea Lion splash! Fk N Fk N F|| =mg sinθ θ F|| mg cosθ θ Free body diagram θ W=mg W=mg Resolve the weight force into two components – parallel and perpendicular to ramp. Result: - Down slope force F|| = m g sin θ - Normal force N = m g cos θ Introduction Section 0 Lecture 1 Slide 26 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 26 N Fk Net force down slope: F||=mg sinθ Fnet = F|| - Fk mg cosθ =ma but friction, Fk = μk N = μk mg cosθ θ W=mg Thus: Fnet = m g sinθ – μk m g cosθ = m a a = g (sinθ - μk cosθ) For θ = 23º, μk= 0.26, g = 9.81 m/s2, then a = 9.81 (sin 23º - 0.26 x cos23º) a = 1.5 m/s2 (note: ‘a’ is independent of mass) Introduction Section 0 Lecture 1 Slide 27 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 27 Physics of Technology PHYS 1800 Lecture 8 Mass & Weight Motion with Friction Introduction Section 0 Lecture 1 Slide 28 More Complex Problems in Statics and Dynamics INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 28 Newton Provided Both the Ideas and the Methods 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 1 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) Slide 29 Galileo Galilei (7)* Copernicus (9) Kepler (10) Tyco Brahe (22) Aristole (an honorable mentioned)*** Mass & Weight Friction Lecture 8-9 Slide 29 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 30 STEEPENS with increasing time. Uniform increase in VG with time As NO horizontal acceleration the ball moves equal distances horizontally in equal time (assuming NO air resistance). INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass & Weight Friction Lecture 8-9 Slide 30 Physics of Technology Next Lab/Demo: Forces Thursday 1:30-2:45 ESLC 53 Ch 3 Next Class: Wednesday 10:30-11:20 Slide 31 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 Mass & Weight Friction Lecture 8-9 Slide 31