1. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 1 Lecture 8-9 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 8 Mass & Weight Motion with Friction

2. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 2 Lecture 8-9 Slide 2 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet *Homework Handout

3. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 3 Lecture 8-9 Slide 3 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 8 Mass & Weight Motion with Friction Introduction and Review

4. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 4 Lecture 8-9 Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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.

5. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 5 Lecture 8-9 Slide 5 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws in Review 1 st Law —a special case of the 2 nd Law for statics, with a=0 or F net =0 An objects velocity remains unchanged, unless a force acts on the object. 2 nd Law (and 1 st 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. 3 rd Law —Forces come from interactions with other objects. For every action (force), there is an equal but opposite reaction (force).

6. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 6 Lecture 8-9 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 imposed force.

7. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 7 Lecture 8-9 Slide 7 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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.

8. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 8 Lecture 8-9 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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. Force has dimensions of (MLT -2 )

9. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 9 Lecture 8-9 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 8 Mass & Weight Motion with Friction Mass & Weight

10. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 10 Lecture 8-9 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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?

11. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 11 Lecture 8-9 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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. The units of mass are kilograms (kg).

12. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 12 Lecture 8-9 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 gravity, an object has no weight but still has the same mass.

13. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 13 Lecture 8-9 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass Standard The International Prototype Kilogram (“IPK”) is the kilogram. It sits next to an inch- based ruler for scale. The IPK is made of a platinum-iridium alloy and is stored in a vault at the BIPM in Sèvres, France. How do we determine what the magnitude of a gravitational force (weight) is?

14. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 14 Lecture 8-9 Slide 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Mass, Weight, and Inertia Objects of different mass experience the same gravitational acceleration on Earth: g = 9.8 m/s 2 By Newton’s 2 nd Law, F = ma, the weight is W = mg. Different gravitational forces (weights) act on falling objects of different masses, but the objects have the same acceleration.

15. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 15 Lecture 8-9 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Weight Example: A body of mass 100 kg on the moon weighs: W = m. g= 100 x 9.8 / 6 =163 N Note: In English (imperial) system, weight (W) is measured in lbs (pounds) – which is also a force. 1 lbs = 4.45 N A mass of 1 kg therefore weighs 2.2 lbs near Earth’s surface (or 9.8 N). (Compared with 980 N on Earth) so, W = 163 N= 36.6 lbs only!

16. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 16 Lecture 8-9 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 8 Mass & Weight Motion with Friction A closer Look at Forces

17. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 17 Lecture 8-9 Slide 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 exerts on an object.

18. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 18 Lecture 8-9 Slide 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 An uncompressed spring and the same spring supporting a book. The compressed spring exerts an upward force on the book. Third-Law Action/Reaction Pair

19. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 19 Lecture 8-9 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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). Compression on an Atomic Scale F spring =-k Δx + + + + + + + + +

20. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 20 Lecture 8-9 Slide 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Third-Law Action/Reaction Pair The car pushes against the road, and the road, in turn, pushes against the car.

21. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 21 Lecture 8-9 Slide 21 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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. contact points Two objects in contact supported by a few high spots or “prominences”.

22. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 22 Lecture 8-9 Slide 22 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 –Presence of lubricants… Lubricants act to separate the two surfaces and allow them to “float” – greatly reducing the friction.

23. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 23 Lecture 8-9 Slide 23 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 8 Mass & Weight Motion with Friction Introduction and Review

24. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 24 Lecture 8-9 Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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). What’s left is the net force. Net force (and masses)  a. A plus initial conditions  motion!

25. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 25 Lecture 8-9 Slide 25 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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  The velocity is then at its maximum value, the terminal velocity

26. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 26 Lecture 8-9 Slide 26 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Example: Sea Lion splash! Resolve the weight force into two components – parallel and perpendicular to ramp. θ θ FkFk F || N W = m g mg cosθ W=mg N FkFk = mg sinθ Free body diagram Result: - Down slope force F || = m g sin θ F || θ - Normal force N = m g cos θ

27. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 27 Lecture 8-9 Slide 27 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 θ N mg cosθ W=mg FkFk F || = mg sinθ Net force down slope: F net = F || - F k = m a but friction, F k = μ k N = μ k mg cosθ Thus: F net = m g sinθ – μ k m g cosθ = m a a = g (sinθ - μ k cosθ) a = 9.81 (sin 23º - 0.26 x cos23º) a = 1.5 m/s 2 (note: ‘a’ is independent of mass) For θ = 23º, μ k = 0.26, g = 9.81 m/s 2, then

28. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 28 Lecture 8-9 Slide 28 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 8 Mass & Weight Motion with Friction More Complex Problems in Statics and Dynamics

29. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 29 Lecture 8-9 Slide 29 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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) Simmon’s list of most influential scientists in the history of the world Newton (1)* (and 2 and 6 and 40) Einstein (2) Galileo Galilei (7)* Copernicus (9) Kepler (10) Tyco Brahe (22) Aristole (an honorable mentioned)***

30. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 30 Lecture 8-9 Slide 30 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 How does this trajectory happen? Key: - resolve motion into its HORIZONTAL and VERTICAL components. But we know V G increases with time due to gravity acceleration! At any instant the total velocity is vector sum of V H and V G Resultant TRAJECTORY STEEPENS with increasing time. As NO horizontal acceleration the ball moves equal distances horizontally in equal time (assuming NO air resistance). V H = constant V G (due to gravity) V TOTAL Uniform increase in V G with time V H (constant)

31. Mass & Weight Friction Introduction Section 0 Lecture 1 Slide 31 Lecture 8-9 Slide 31 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology Next Lab/Demo: Forces Thursday 1:30-2:45 ESLC 53 Ch 3 Next Class: Wednesday 10:30-11:20 BUS 318 room Read Ch 4