PHYS 34210 PHYSICS I Notre Dame, London Programme, Fall 2013

1. REGAN PHY34210 PHYS 34210 PHYSICS I Notre Dame, London Programme, Fall 2013 Prof. Paddy Regan Dept. of Physics, University of Surrey, Guildford, GU2 7XH, UK E-Mail: p.regan@surrey.ac.uk

2. REGAN PHY34210 Course & General Information • Lectures, usually, Tuesdays 2.15-5.00 • first lecture Tues 27th August 2010 • One ‘makeup’ lecture Mon. 30th Sept. 5.15 – 8pm (no class on Tues. 29th Oct) • Grading • 3 x 2 hour class examinations • Exam 1 : Tues. 24th September (30%); • Exam 2: Tues 5th November (35%), • Exam 3: Tues. 26th November (35%) • Some information about Prof. Paddy Regan FInstP CPhys: • National Physical Lab. & University of Surrey Chair Professor in Radionuclide Metrology, (staff since 1994). • BSc University of Liverpool (1988); DPhil University of York (1991). • Adjunct Assoc. Prof. at ND London 2002-7; Full Professor from 2007 - present • Held post-doctoral research positions at: • University of Pennsylvania, Philadelphia, USA (1991-2) • Australian National University, Canberra, Australia (1992-4); • Yale University (sabbatical researcher 2002 ; Flint Visiting Research Fellow 2004 – 2013) • Co-author of >200 papers in nuclear physics; supervised 25 PhD students so far + 100 Masters. • Led RISING and PreSPEC projects (major nuclear physics research project at GSI, Germany). • Married (to a nurse), 4 kids. • Understands gridiron, baseball, (ice) hockey etc., regular visitor to US (and other countries) • Still plays squash and golf (poor, 27); formerly football (soccer), cricket & a bit of rugby (union). • Occasional half marathons for the mental health charity, MIND (see • http://uk.virginmoneygiving.com/Paddy-James-Clare-Regan • Have also done some (physics related) media work in the UK and USA, see e.g., • http://www.bbc.co.uk/news/world-asia-pacific-12744973

3. REGAN PHY34210 Course textbook, Fundamentals of Physics, Halliday, Resnick & Walker, published by Wiley & Sons. Now in 9th Edition. http://www.wiley.com/WileyCDA/WileyTitle/productCd-EHEP001575.html

4. REGAN PHY34210 REGAN PHY34210 4 Course Timetable (2013) PART 1 PART 3 PART 2 Lect 1: 27 Aug (Cp 1,2) Lect 2: 03 Sept (Cp 3,4) Lect 3: 10 Sept (Cp 5,6) Lect 4: 17 Sept (revision) Lect 5: 24 Sept Exam 1 * Lect 6: Mon. 30th Sept. (Ch. 7,8) 5.15 - 8pm * Lect 7: 01 Oct (Ch 9,10) * Lect 8: 08 Oct. (Ch 11,12) * Lect 9: 15 Oct. (revision) Break, no lect. 22nd Oct. No lect. 29th Oct (resched). * Lect 10: 5th Nov Exam 2 Lect 11: 12 Nov. (13,14) Lect 12: 19 Nov. (15,16) Lect 13: Weds. 20 Nov (17,18) 5.15-8pm. Lect 14: 26 Nov Exam 3 Course notes and past papers/solns can be found at the following link: http://personal.ph.surrey.ac.uk/~phs1pr/lecture_notes/notre_dame/

5. 1: Measurement Units, length, time, mass 2: Motion in 1 Dimension displacement, velocity, acceleration 3: Vectors adding vectors & scalars, components, dot and cross products 4: Motion in 2 & 3 Dimensions position, displacement, velocity, acceleration, projectiles, motion in a circle, relative motion 5: Force and Motion: Part 1 Newton’s laws, gravity, tension 6: Force and Motion: Part 2 Friction, drag and terminal speed, motion in a circle REGAN PHY34210 1st Section:

6. 7: Kinetic Energy and Work Work & kinetic energy, gravitational work, Hooke’s law, power. 8: Potential Energy and Conservation of Energy Potential energy, paths, conservation of mechanical energy. 9: Systems of Particles Centre of mass, Newton’s 2nd law, rockets, impulse, 10: Collisions. Collisions in 1 and 2-D 11 : Rotation angular displacement, velocity & acceleration, linear and angular relations, moment of inertia, torque. 12: Rolling, Torque and Angular Momentum KE, Torque, ang. mom., Newton’s 2nd law, rigid body rotation REGAN PHY34210 2nd Section:

7. REGAN PHY34210 3rd section: • 13: Equilibrium and Elasticity • equilibrium, centre of gravity, elasticity, stress and strain. • 14: Gravitation • Newton’s law, gravitational potential energy, Kepler’s laws. • 15: Fluids • density and pressure, Pascal’s principle, Bernoulli’s equation. • 16 : Oscillations • Simp. Harm. Mo. force and energy, pendulums, damped motion. • 17 & 18 : Waves I and II • Types of Waves, wavelength and frequency, interference, standing waves, sound waves, beats, Doppler effect.

8. REGAN PHY34210 Recommended Problems and Lecture Notes. Problems are provided at the end of each book chapter. Previous years examinations papers will also be provided with solutions (later) for students to work through at their leisure. No marks will be give for these extra homework problems Final grade will come from the three class exams. Full lecture notes can be found on the web at http://www.ph.surrey.ac.uk/~phs1pr/lecture_notes/phy34210_13.ppt and http://www.ph.surrey.ac.uk/~phs1pr/lecture_notes/phy34210_13.pdf

9. REGAN PHY34210 1: Measurement Physical quantities are measured in specific UNITS, i.e., by comparison to a reference STANDARD. The definition of these standards should be practical for the measurements they are to describe (i.e., you can’t use a ruler to measure the radius of an atom!) Most physical quantities are not independent of each other (e.g. speed = distance / time). Thus, it often possible to define all other quantities in terms of BASE STANDARDS including length (metre), mass (kg) and time (second).

10. REGAN PHY34210 SI Units The 14th General Conference of Weights and Measures (1971) chose 7 base quantities, to form the International System of Units (Systeme Internationale = SI). There are also DERIVED UNITS, defined in terms of BASE UNITS, e.g. 1 Watt (W) = unit of Power = 1 Kg.m2/sec2 per sec = 1 Kg.m2/s3 Scientific Notation In many areas of physics, the measurements correspond to very large or small values of the base units (e.g. atomic radius ~0.0000000001 m). This can be reduced in scientific notation to the ‘power of 10’ ( i.e., number of zeros before (+) or after (-) the decimal place). e.g. 3,560,000,000m = 3.56 x 109 m = 3.9 E+9m & 0.000 000 492 s = 4.92x10-7 s = 4.92 E-7s

11. REGAN PHY34210 Prefixes For convenience, sometimes, when dealing with large or small units, it is common to use a prefix to describe a specific power of 10 with which to multiply the unit. e.g. 1000 m = 103 m = 1E+3 m = 1 km 0.000 000 000 1 m = 10-10 m = 0.1 nm • 1012 = Tera = T • 109 = Giga = G • 106 = Mega = M • 103 = Kilo = k • 10-3 = milli = m • 10-6 = micro = m • 10-9 = nano = n • 10-12 = pico = p • 10-15 = femto = f

12. REGAN PHY34210 Converting Units It is common to have to convert between different systems of units (e.g., Miles per hour and metres per second). This can be done most easily using the CHAIN LINK METHOD, where the original value is multiplied by a CONVERSION FACTOR. NB. When multiplying through using this method, make sure you keep the ORIGINAL UNITS in the expression e.g., 1 minute = 60 seconds, therefore (1 min / 60 secs) = 1 and (60 secs / 1 min) = 1 Note that 60 does not equal 1 though! Therefore, to convert 180 seconds into minutes, 180 secs = (180 secs) x (1 min/ 60 secs) = 3 x 1 min = 3 min.

13. REGAN PHY34210 Length (Metres) Original (1792) definition of a metre (meter in USA!) was 1/10,000,000 of the distance between the north pole and the equator. Later the standards was changed to the distance between two lines on a particular standard Platinum-Iridium bar kept in Paris. (1960) 1 m redefined as 1,650,763.73 wavelengths of the (orange/red) light emitted from atoms of the isotope 86Kr. (1983) 1 m finally defined as the length travelled by light in vacuum during a time interval of 1/299,792,458 of a second. • To Andromeda Galaxy ~ 1022 m • Radius of earth ~ 107 m • Adult human height ~ 2 m • Radius of proton ~ 10-15 m

14. REGAN PHY34210 Time (Seconds) Standard definitions of the second ? Original definition 1/(3600 x 24) of a day, 24 hours = 1day, 3600 sec per hours, thus 86,400 sec / day, 3651/4 days per year and 31,557,600 sec per year. From HRW, p6 But, a day does not have a constant duration! (1967) Use atomic clocks, to define 1 second as the time for 9,192,631,770 oscillations of the light of a specific wavelength (colour) emitted from an atom of caesium (133Cs)

15. REGAN PHY34210 Mass (Kg, AMU) 1 kg defined by mass of Platinum-Iridium cylinder near to Paris. Masses of atoms compared to each other for other standard. Define 1 atomic mass unit = 1 u (also sometimes called 1 AMU) as 1/12 the mass of a neutral carbon-12 atom. 1 u = 1.66054 x 10-27 kg Orders of Magnitude It is common for physicists to ESTIMATE the magnitude of particular property, which is often expressed by rounding up (or down) to the nearest power of 10, or ORDER OF MAGNITUDE, e.g.. 140,000,000 m ~ 108m,

16. REGAN PHY34210 Estimate Example 1: A ball of string is 10 cm in diameter, make an order of magnitude estimate of the length, L , of the string in the ball. r d d

17. d h q r r REGAN PHY34210 E.g., 2: Estimate Radius of Earth (from the beach.) q is the angle through which the sun moves around the earth during the time between the ‘two’ sunsets (t ~ 10 sec).

18. The DISPLACEMENT, Dx is the change from one position to another, i.e., Dx= x2-x1. Positive values of Dx represent motion in the positive direction (increasing values of x, i.e. left to right looking into the page), while negative values correspond to decreasing x. x = -3 -2 -1 0 1 2 3 REGAN PHY34210 Position and Displacement. 2: Motion in a Straight Line To locate the position of an object we need to define this RELATIVE to some fixed REFERENCE POINT, which is often called the ORIGIN (x=0). In the one dimensional case (i.e. a straight line), the origin lies in the middle of an AXIS (usually denoted as the ‘x’-axis) which is marked in units of length. Note that we can also define NEGATIVE co-ordinates too. Displacement is a VECTOR quantity. Both its size (or ‘magnitude’) AND direction (i.e. whether positive or negative) are important.

19. REGAN PHY34210 Average Speed and Average Velocity We can describe the position of an object as it moves (i.e. as a function of time) by plotting the x-position of the object (Armadillo!) at different time intervals on an (x , t) plot. The average SPEED is simply the total distance travelled (independent of the direction or travel) divided by the time taken. Note speed is a SCALAR quantity, i.e., only its magnitude is important (not its direction). From HRW

20. REGAN PHY34210 The average VELOCITY is defined by the displacement (Dx) divided by the time taken for this displacement to occur (Dt). The SLOPE of the (x,t) plot gives average VELOCITY. Like displacement, velocity is a VECTOR with the same sign as the displacement. The INSTANTANEOUS VELOCITY is the velocity at a specific moment in time, calculated by making Dt infinitely small (i.e., calculus!)

21. The instantaneous ACCELERATION is given by a, where, SI unit of acceleration is metres per second squared (m/s2) REGAN PHY34210 Acceleration HRW Acceleration is a change in velocity (Dv) in a given time (Dt). The average acceleration, aav, is given by

22. By making the assumption that the acceleration is a constant, we can derive a set of equations in terms of the following quantities REGAN PHY34210 Constant Acceleration and the Equations of Motion For some types of motion (e.g., free fall under gravity) the acceleration is approximately constant, i.e., if v0 is the velocity at time t=0, then Usually in a given problem, three of these quantities are given and from these, one can calculate the other two from the following equations of motion.

23. REGAN PHY34210 Equations of Motion (for constant a).

24. REGAN PHY34210 Alternative Derivations (by Calculus)

25. REGAN PHY34210 Free-Fall Acceleration At the surface of the earth, neglecting any effect due to air resistance on the velocity, all objects accelerate towards the centre of earth with the same constant value of acceleration. This is called FREE-FALL ACCELERATION, or ACCELERATION DUE TO GRAVITY, g. At the surface of the earth, the magnitude of g = 9.8 ms-2 Note that for free-fall, the equations of motion are in the y-direction (i.e., up and down), rather than in the x direction (left to right). Note that the acceleration due to gravity is always towards the centre of the earth, i.e. in the negative direction, a= -g = -9.8 ms-2

26. (a) since a= -g = -9.8ms-2, initial position is y0=0 and at the max. height vm a x=0 Therefore, time to max height from (b) REGAN PHY34210 Example A man throws a ball upwards with an initial velocity of 12ms-1. (a) how long does it take the ball to reach its maximum height ? (b) what’s the ball’s maximum height ?

27. REGAN PHY34210 ( c) How long does the ball take to reach a point 5m above its initial release point ? Note that there are TWO SOLUTIONS here (two different ‘roots’ to the quadratic equation). This reflects that the ball passes the same point on both the way up and again on the way back down.

28. REGAN PHY34210 3: Vectors • Quantities which can be fully described just by their size are called SCALARS. • Examples of scalars include temperature, speed, distance, time, mass, charge etc. • Scalar quantities can be combined using the standard rules of algebra. • A VECTOR quantity is one which need both a magnitude (size) and direction to be complete. • Examples of vectors displacement, velocity, acceleration, linear and angular momentum. • Vectors quantities can be combined using special rules for combining vectors.

29. Note that two vectors can be added together in either order to get the same result. This is called the COMMUTATIVE LAW. Generally, if we have more than 2 vectors, the order of combination does not affect the result. This is called theASSOCIATIVE LAW. = REGAN PHY34210 Adding Vectors Geometrically Any two vectors can be added using the VECTOR EQUATION, where the sum of vectors can be worked out using a triangle.

30. REGAN PHY34210 Subtracting Vectors, Negative Vectors Note that as with all quantities, we can only add / subtract vectors of the same kind (e.g., two velocities or two displacements). We can not add differing quantities e.g., apples and oranges!)

31. y x REGAN PHY34210 A simple way of adding vectors can be done using their COMPONENTS. The component of a vector is the projection of the vector onto the x, y (and z in the 3-D case) axes in the Cartesian co-ordinate system. Obtaining the components is known as RESOLVING the vector. The components can be found using the rules for a right-angle triangle. i.e. Components of Vectors

32. A UNIT VECTOR is one whose magnitude is exactly equal to 1. It specifies a DIRECTION. The unit vectors for the Cartesian co-ordinates x,y and z are given by, z 1 x 1 y 1 REGAN PHY34210 Unit Vectors The use of unit vectors can make the addition/subtraction of vectors simple. One can simply add/subtract together the x,y and z components to obtain the size of the resultant component in that specific direction. E.g,

33. REGAN PHY34210 There are TWO TYPES of vector multiplication. One results in a SCALAR QUANTITY (the scalar or ‘dot’ product). The other results in a VECTOR called the vector or ‘cross’ product. Vector Multiplication For the SCALAR or DOT PRODUCT,

34. The VECTOR PRODUCT of two vectors and produces a third vector whose magnitude is given by The direction of the resultant is perpendicular to the plane created by the initial two vectors, such that f is the angle between the two initial vectors f REGAN PHY34210 Vector (‘Cross’) Product

35. y q x REGAN PHY34210 Example 1:

36. REGAN PHY34210 Example 2:

37. REGAN PHY34210 4: Motion in 2 and 3 Dimensions The use of vectors and their components is very useful for describing motion of objects in both 2 and 3 dimensions. Position and Displacement

38. The average velocity is given by While the instantaneous velocity is given by making Dt tend to 0, i.e. Similarly, the average acceleration is given by, While the instantaneous acceleration is given by REGAN PHY34210 Velocity and Acceleration

39. The specialist case where a projectile is ‘launched’ with an initial velocity, and a constant free-fall acceleration, . Examples of projectile motion are golf balls, baseballs, cannon balls. (Note, aeroplanes, birds have extra acceleration see later). REGAN PHY34210 Projectile Motion We can use the equations of motion for constant acceleration and what we have recently learned about vectors and their components to analyse this type of motion in detail. More generally,

40. Vertical Motion vy REGAN PHY34210 In the projectile problem, there is NO ACCELERATION in the horizontal direction (neglecting any effect due to air resistance). Thus the velocity component in the x (horizontal) direction remains constant throughout the flight, i.e., Horizontal Motion

41. REGAN PHY34210 The Equation of Path for Projectile Motion Note that this is an equation of the form y=ax+bx2i.e., a parabola (also, often y0=x0=0.)

42. vy=0 Max height (y0,x0) Range REGAN PHY34210 The Horizontal Range

43. R How far must the fence be moved back for no homers to be possible ? REGAN PHY34210 At what angle must a baseball be hit to make a home run if the fence is 150 m away ? Assume that the fence is at ground level, air resistance is negligible and the initial velocity of the baseball is 50 m/s. Example

44. REGAN PHY34210 Uniform Circular Motion A particle undergoes UNIFORM CIRCULAR MOTION is it travels around in a circular arc at a CONSTANT SPEED. Note that although the speed does not change, the particle is in fact ACCELERATING since the DIRECTION OF THE VELOCITY IS CHANGING with time. The velocity vector is tangential to the instantaneous direction of motion of the particle. The (centripetal) acceleration is directed towards the centre of the circle Radial vector (r) and the velocity vector (v) are always perpendicular

45. REGAN PHY34210 Proof for Uniform Circular Motion yp q xp

46. p B A If we assume that different FRAMES OF REFERENCE always move at a constant velocity relative to each other, then using vector addition, i.e., acceleration is the SAME for both frames of reference! (if VAB=const)! REGAN PHY34210 If we want to make measurements of velocity, position, acceleration etc. these must all be defined RELATIVE to a specific origin. Often in physical situations, the motion can be broken down into two frames of reference, depending on who is the OBSERVER. ( someone who tosses a ball up in a moving car will see a different motion to someone from the pavement). Relative Motion

47. Note that Newtonian mechanics breaks down for (1) very fast speeds, i.e. those greater than about 1/10 the speed of light c, c=3x108ms-1 where it is replaced by Einstein’s theory of RELATIVITY and (b) if the scale of the particles is very small (~size of atoms~10-10m), where QUANTUM MECHANICS is used instead. Newton’s Laws are limiting cases for both quantum mechanics and relativity, which are applicable for specific velocity and size regimes REGAN PHY34210 5: Force and Motion (Part 1) If either the magnitude or direction of a particle’s velocity changes (i.e. it ACCELERATES), there must have been some form of interaction between this body and it surroundings. Any interaction which causes an acceleration (or deceleration) is called a FORCE. The description of how such forces act on bodies can be described by Newtonian Mechanics first devised by Sir Isaac Newton (1642-1712)..

48. This means that (a) if a body is at rest, it will remain at rest unless acted upon by an external force, it; and (b) if a body is moving, it will continue to move at that velocity and in the same direction unless acted upon by an external force. REGAN PHY34210 Newton’s First Law Newton’s 1st law states ‘ If no force acts on a body, then the body’s velocity can not change, i.e., the body can not accelerate’ So for example, (1) A hockey puck pushed across a ‘frictionless’ rink will move in a straight line at a constant velocity until it hits the side of the rink. (2) A spaceship shot into space will continue to move in the direction and speed unless acted upon by some (gravitational) force.

49. If two or more forces act on a body we can find their resultant value by adding them as vectors. This is known as the principle of SUPERPOSITION. This means that the more correct version of Newton’s 1st law is ‘ If no NET force acts on a body, then the body’s velocity can not change, i.e., the body can not accelerate’ REGAN PHY34210 Force The units of force are defined by the acceleration which that force will cause to a body of a given mass. The unit of force is the NEWTON (N) and this is defined by the force which will cause an acceleration of 1 m/s2 on a mass of 1 kg. Mass:we can define the mass of a body as the characteristic which relates the applied force to the resulting acceleration.

50. As with other vector equations, we can make three equivalent equations for the x,y and z components of the force. i.e., The acceleration component on each axis is caused ONLY by the force components along that axis. REGAN PHY34210 Newton’s 2nd Law Newton’s 2nd law states that ‘ The net force on a body is equal to the product of the body’s mass and the acceleration of the body’ We can write the 2nd law in the form of an equation: