Welcome to PHYS 172H

Transcription

1 Welcome to PHYS 172H Course web page: go to and select Phys 172H Textbook: Matter & Interactions Volume 1 Modern Mechanics by Ruth Chabay and Bruce Sherwood (Wiley); 3d edition. Lab Manual: Aailable free on the website. WebAssign: (homework) go to: CHIP: scoring and grades i>clicker: Go to the course web page, register on CHIP Help center room 11 All necessary course information is to be found on the 172H webpage

2 Grades Eening Mid-Term Exams (3x100) 300 Final Exam (comprehensie) 200 Labs 150 Homework (WebAssign) 150 Clicker questions and attendance 50 Recitation quizzes and worksheets 150 TOTAL 1000 See syllabus: Absences and excused grades

3 Matter and Interactions Goal: use small set of fundamental principles to explain broad range of phenomena Chapter 1 Interactions and Motions Topics: Kinds of matter we deal with How to detect interaction Quantitatie description of position and motion in 3D space Momentum

4 Kinds of matter Atoms Nuclei =1 Å (Angström)

5 Kinds of matter Molecules: Seeral atoms bound together The physical and chemical properties of a molecule differ from those of the constituent atoms H 2 O - water C60 (soccer ball molecule) Also called Buckyballs for the architect and inentor Buckminster Fuller, who Inented the Geodesic Dome. Protein molecule (myoglobin)

6 Kinds of matter Solids: Billions of atoms or molecules come together Atoms are fixed in 3D array Salt crystal Silicon crystal STM images Amorphous Germanium

7 Kinds of matter Liquids: Atoms are still bound to each other but can freely slide along each other Water Dynamics is complex: we will not consider in detail in this course

8 Kinds of matter Gases: Atoms are not bound to each other Energy of atoms is too large and Interatomic forces are broken

9 Detecting interactions Objects made of matter interact with each other: Graitationally Electrically Magnetically Through the strong and weak nuclear interactions Detecting some kinds of interaction: Change of speed Change of direction Change of elocity Velocity: a physical quantity that has magnitude and direction (speed) ector

10 Motion Non-uniform motion Velocity changes in time Uniform motion: elocity is constant Special case: an object at rest (elocity is zero, direction undefined) Uniform motion implies that there is no net interaction

11 Newton s first law of motion uniform (constant) elocity Isaac Newton An object moes in a straight line and at constant speed except to the extent that it interacts with other objects The stronger the interaction, the faster the change in elocity Object at rest is a case of uniform elocity This is a qualitatie law

12 Newton s first law of motion and eeryday life Example: Pushing a car at uniform elocity Need to push (or pull) constantly to cancel graitational interaction and friction

13 Indicators of interaction Change of elocity Examples: Change of identity H 2 + O 2 H 2 O Change of shape bending a wire Change of temperature heating pot of water on a hot stoe Lack of change when change is expected balloon floating in sky Existence of solids and liquids requires BONDING, which is an interlaction The fact that you aren t floating away from your seats implies that graity is acting on you, which is an interaction between you and the mass of the Earth Interactions can cause change. BUT no change does not necessarily mean no interactions are present. Now let s study motions of objects, where interactions are rather obious.

14 Describing 3D world: Vectors Scalar: a quantity represented by a single number Vector: a quantity represented by more than one number, encoding magnitude and direction Right-handed Cartesian 3D coordinate system (meaning if you curl your fingers from X to Y, your Thumb points along Z; RIGHT hand, please!) To describe position we will use a ector that points from origin to location point Vector r is defined by its 3 Cartesian components: r = r, r, r = 4, 3, 2 m x y z r x = 4 m r y = 3 m r z = 2 m x, y and z components of a ector Note: in 2D space (surface) a ector is represented by 2 components

15 Equal ectors r = r, r, r = 4, 3, 2 m r x = 4 m r y = 3 m r z = 2 m x y z Equal ectors: all components are equal r x = 4 m r y = 3 m r z = 2 m Note: a component of a ector specifies the difference between the respectie coordinate of the tip and that of the tail In other words, you can slide a ector around parallel to itself and it remains the same ector

16 Magnitude of a ector (courtesy of Mr. Pythagoras) r = r, r, r = 4, 3, 2 m x y z Magnitude = length of a ector: ( ) m + (3 m) + (2 m) = 29m= 5.39m r = r, r, r then r = r + r + r x y z x y z magnitude (scalar) Can magnitude of a ector be negatie? Can a ector be negatie or positie?

17 Vectors: math operations Legal: r r Addition a+ w r r Subtraction a w Magnitude a r Unit ector â this is ector a diided by its length Multiply /diide with scalar 3a r r r Δ dr Find rate of change or Δt dt Not legal: Vector cannot be equal to scalar Vector cannot be added-to/subtracted-from scalar Cannot diide by ector

18 Vectors: multiply by a scalar The magnitude (length) of the ector changes The direction stays the same (or changes to opposite) r = x, y, z then ar = ax, ay, az ar = a r x y z = x, yz then =,, b b b b

19 Vectors: unit ector The ector with magnitude =1 Is ector <1,1,1> a unit ector? r = r + r + r = = x y z We can use the fact that 1 1 r = 3 3 r Unit ector: 1 1 1,, Calculating unit ector for any ector: r rx, ry, rz r r x y rz rˆ = = =,, r r + r + r r + r + r r + r + r r + r + r x y z x y z x y z x y z

20 Vectors: special unit ectors ˆr r Special unit ectors points along axes x, y and z: iˆ = 1, 0, 0 ˆj = 0,1, 0 kˆ = 0, 0,1 (i-hat) Any ector can be expressed as a sum of the three scaled unit ectors: r = r, r, r ˆ ˆ z = rxi + rj y + r x y z Any ector can be expressed as a scalar multiplied by a unit ector r = r, r, r = r rˆ x y z kˆ

21 Vectors: addition A= Ax, Ay, Az B= Bx, By, Bz A + B= A + B A + B A + B ( ),( ),( ) x x y y z z

22 Vectors: subtraction A = A, A, A B = B, B, B x y z x y z A B = A B, A B, A B, ( ) ( ) ( ) x x y y z z

23 Zero ector r 0= 0,0,0 Magnitude = 0 Direction: undefined Example: r r A A A= 0 A

24 Change in quantity Change in ector: Δ r = r r What are the components of Δr? f i r i Δr r f Change in scalar: Δ t = t t f i