Be on time Switch off mobile phones. Put away laptops. Being present = Participating actively

Transcription

1 A couple of house rules Be on time Switch off mobile phones Put away laptops Being present = Participating actively

2 Het basisvak Toegepaste Natuurwetenschappen Applied Natural Sciences Leo Pel e mail: 3nab0@tue.nl

3 Content of the course 3NAB0 (see study guide) November diagnostic test! Week 1 : 13 November Week 2 : 20 November Introduction, units (Ch1), Circuits (Ch25,26) Heat (Ch17), Kinematics (Ch2 3) Week 3: 27 November Newton, Energy (Ch4 6) Week 4: 4 December Energy, Momentum (Ch7 8) 7 December Intermediate assessment Week 5: 11 December Week 6: 18 December Week 7: 8 January (2016) Rotation, Elasticity, Fluid mechanics (Ch9 12) Harmonic oscillator and Waves (Ch14 15) Sound (Ch16) Light (Ch33) 24 January Final assessment

4 Chapter 1 Units, Physical Quantities, and Vectors PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Copyright 2012 Pearson Education Inc.

5 LEARNING GOALS Three fundamental quantities of physics and the units physicists use to measure them. The difference between scalars and vectors, and how to add and subtract vectors graphically. What the components of a vector are, and how to use them in calculations. What unit vectors are, and how to use them with components to describe vectors.

6 Physics and the Laws of Nature Physics: the study of the relations between physical quantities, expressed as fundamental laws of nature. These laws can be expressed as mathematical equations. (e.g., F = m a) Most physical quantities have units, which must match on both sides of an equation. Much complexity can arise from even relatively simple physical laws.

7 Solving problems in physics A problem solving strategy offers techniques for setting up and solving problems efficiently and accurately.

8 Solving problems in physics No recipe or plug-and-chug works all the time, but here are some guidelines: 1. Read the problem carefully. 2. Draw a sketch of the system. 3. Visualize the physical process involved. 4. Devise a strategy for solving the problem. 5. Identify the appropriate equations. 6. Solve the equations. Calculate the answer. 7. Check your answer. Dimensions? Reasonable? 8. Explore the limits and special cases.

9 Chapter 1: quantities, units, vectors To any physical quantity there belongs a unit and a dimension. quantity SI unit dimension length (l) meter (m) L time (t) second (s) T mass (m) kilogram (kg) M All quantities in mechanics can be expressed in these three units

10 The SI Time Unit: second (s) 13 th Century Water Clock Cesium Fountain Clock The second was originally defined as (1/60)(1/60)(1/24) of a mean solar day. Currently, 1 second is defined as 9,192,631,770 oscillations of the radio waves absorbed by a vapor of cesium-133 atoms. This is a definition that can be used and checked in any laboratory to great precision.

11 The SI Length Unit: meter (m) The meter was originally defined as 1/10,000,000 of the distance from the Earth s equator to its North pole on the line of longitude that passes through Paris. For some time, it was defined as the distance between two scratches on a particular platinum-iridium bar located in Paris. Currently, 1 meter is defined as the distance traveled by light in 1/299,792,458 of a second

12 The SI Mass Unit: kilogram The kilogram was originally defined as the mass of 1 liter of water at 4 o C. Currently, 1 kilogram is the mass of the international standard kilogram, a polished platinum-iridium cylinder stored in Sèveres, France. (It is currently the only SI unit defined by a manufactured object.) Question: In a telephone conversation, could you accurately describe to a member of a alien civilization how big a kilogram was? Answer: More or less. Avagadro s number of carbon-12 atoms ( x ) has a mass of exactly grams.

13 New Kg standard Kibble balance: This instrument uses Planck s constant to define the kg h= x kg m 2 /s. An electrical current is sent through a coiled wire, generating a magnetic field that creates the upward force needed to balance the scale. One can figure out the strength of that field by pulling on the coil. If you know the voltage, the current and the velocity at which the coil was pulled, you can calculate the Planck constant with extreme precision.

14 Dimensions and Units

15 Metric prefixes peta P = 1,000,000,000,000,000 tera T = 1,000,000,000,000 giga G 10 9 = 1,000,000,000 mega M 10 6 = 1,000,000 kilo k 10 3 = 1,000 hecto h 10 2 = 100 deka da 10 1 = 10 deci d 10-1 = 0.1 centi c 10-2 = 0.01 milli m 10-3 = micro µ 10-6 = 0.000,001 nano n 10-9 = 0.000,000,001 pico p = 0,000,000,000,001 femto f = 0.000,000,000,000,001 atto a = 0.000,000,000,000,000,001

16 Dimensional Analysis Any valid physical equation must be dimensionally consistent each side must have the same dimensions. From the Table: Distance = velocity time Velocity = acceleration time Energy = mass (velocity) 2

17 Dimensional Analysis The period P (T) of a swinging pendulum depends only on the length of the pendulum d (L) and the acceleration of gravity g (L/T 2 ). Which of the following formulas for P could be correct? P 2 (dg) 2 P d 2 g (1) (2) (3) P 2 d g

18 Remember that P is in units of time (T), d is length (L) and g is acceleration (L/T 2 ). The both sides must have the same units 2 4 L L L 2 T 4 T T L L T 2 T 2 T L 2 L T 2 T T P 2 dg 2 (a) (b) (c) P d 2 g P 2 d g

19 Order of Magnitude Calculations 1. Make a rough estimate of the relevant quantities to one significant figure, preferably some power of Combine the quantities to make the estimate. 3. Think hard about whether the estimate is reasonable.

20 Order of Magnitude Calculations Television: A person say he/she will still live for another 100,000 days 1. YES 2. NO Answer: days x100 years =

21 Burning rubber Problem: When you drive your car 1 km, estimate the thickness of tire tread that is worn off. Answer: 1. Estimate the distance require to wear down a tire tread to the point where it needs to be replaced: ~60,000 km 2. Estimate the thickness of a typical tire tread lost on a worn tire: ~ 1 cm. 3. Consider the following ratio: 5 1 cm of tread loss cm of tread loss 60,000 km of travel 1 km of travel m of tread loss per km Therefore, a car loses about 2x10-7 m = 0.2 µm of tire tread in driving 1 km.

22 Classical mechanics Isaac Newton ( )) Born the year Galileo died At Woolsthorpe, near Grantham in Lincolnshire, into a poor farming family. Terrible farmer, sent to Cambridge University in 1661 to become preacher. Instead, he studied mathematics. Forced to leave Cambridge from 1665 to 1667 because of the great plague. Newton called this period the Height of his Creative Power. Greatest works were accomplished while he was years old! One of the most influential people who ever lived Newton s Paradigm - now called classical physics - dominated Western thought for more than two centuries

23 LOOK Principia Newton

24 Content

25 First build up of the mathematical tools needed: calculus

26 Example: movement along straight line by force

27 What do we need? 1. Short repetition scalar/vector CH 1: vector operations needed 2. Calculus for description of motion: kinematics CH 2: 1D CH3 : 2D

28 Scalars and Vectors Temperature = Scalar Quantity is specified by a single number giving its magnitude. Velocity = Vector Quantity is specified by three numbers that give its magnitude and direction (or its components in three perpendicular directions).

29 Adding two vectors etc

30 Components of a vector Adding vectors graphically provides limited accuracy. Vector components provide a general method for adding vectors. A x =Acos θ A y = Asin θ, where θ

31 Calculations using components Use the components of a vector to find its magnitude and direction: 2 2 A A Ax Ay and tan A y Use the components of a set of vectors to find the components of their sum: R A B C, R A B C x x x x y y y y x

32 The scalar: dot product The scalar product ( dot product ) of two vectors is

33 Summary

34 Distance in time: daily langauge

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