Physics Mechanics. Lecture 1 Physics and the Laws of Nature

Transcription

1 Physics Mechanics Lecture 1 Physics and the Laws of Nature 1

2 Physics: the study of the fundamental laws of nature These laws can be expressed as mathematical equations. (e.g. F = ma, E=mc 2 ) Most physical quantities have units, which must match on both sides of an equation. Much complexity can arise from even relatively simple physical laws. 2

3 Measurements Basis of testing theories in science Need to have consistent systems of units for the measurements Need rules for dealing with the uncertainties 3

4 Standard International Units Standard International (SI) Units (also known as MKS) Length [L]: meter Mass [M]: m kilogram kg Time [T]: second s Units for almost all other physical quantities can be constructed from mass, length, and time, so these are the fundamental units. 4

5 Unit Conversions English Units are used only in USA, Liberia, and Myanmar. 1 inch = 2.54 cm 1 mile = km 1 pound = kg 1 cm = inch 1 km = mile 1 kg = pound When units are not consistent, you may need to convert to appropriate ones Units can be treated like algebraic quantities that can cancel each other out 5

6 The SI Time Unit: second (s) Cesium 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. 6

7 The SI Length Unit: meter (s) 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 7

8 The SI Mass Unit: Kilogram (kg) The kilogram was originally defined as the mass of 1 liter of water at 4 o C. Currently, 1 kilogram is the mass of a polished platinum-iridium cylinder stored in Sèveres, France. (It is currently the only SI unit defined by a manufactured object.) 8

9 Prefixes Prefixes correspond to powers of 10 Each prefix has a specific name/ abbreviation Power Prefix Abbrev peta P tera T 10 9 giga G 10 6 mega M 10 3 kilo k 10-2 centi c 10-3 milli m 10-6 micro μ 10-9 nano n 9

10 Dimensional Analysis Dimensions for commonly used quantities Length L m (SI) Area L 2 m 2 (SI) Volume L 3 m 3 (SI) Velocity (speed) L/T m/s (SI) Acceleration L/T 2 m/s 2 (SI) Example of dimensional analysis distance = velocity time L = (L/T) T Any valid physical equation must be dimensionally consistent each side must have the same dimensions. 10

11 Dimensional Analysis Dimension denotes the physical nature of a quantity Technique to check the correctness of an equation Dimensions (length, mass, time, combinations) can be treated as algebraic quantities add, subtract, multiply, divide quantities can be added/ subtracted only if have same units Both sides of equation must have the same dimensions 11

12 Example 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? (a) (b) (c) 12

13 Example 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 (a) (b) (c) T= (LxL/T 2 ) 2 T= L 4 /T 4 NO T= L/(L/T 2 ) T= T 2 NO 13 T= (L/(L/T 2 )) 1/2 T= (T 2 ) 1/2 =T YES

14 Unit Conversions 1 inch = 2.54 cm 1 mile = km 1 pound = kg 1 cm = inch 1 km = mile 1 kg = pound 1 mile = 1609 m = km 1 ft = m = cm 1m = in = ft 1 in = m = 2.54 cm When units are not consistent, you may need to convert to appropriate ones Units can be treated like algebraic quantities that can cancel each other out 14

15 Uncertainty in Measurements All measurements are approximations no measuring device can give perfect measurements without experimental uncertainty. There is uncertainty in every measurement, this uncertainty carries over through the calculations need a technique to account for this uncertainty We will use rules for significant figures to approximate the uncertainty in results of calculations 15

16 Uncertainty in Measurements A significant figure is one that is reliably known. All non-zero digits are significant Zeros are significant when between non zero digits (101) after the decimal point and after a non zero digit (ex ) Ex. mass 13.2 g (+/- 0.1 g) => 3 sig fig, g => 4 sig fig, => 4 sig fig, 1320 => 4 sig dig 0.01 g => 1 sig fig, g => 1 sig fig, 0.20 g => 2 sig fig 16

17 Operations with Significant Figures Accuracy -- number of significant figures When multiplying or dividing, round the result to the same accuracy as the least accurate measurement Example: rectangular plate: 4.5 cm by 7.3 cm area: cm 2 33 cm 2 When adding or subtracting, round the result to the smallest number of decimal places of any term in the sum Example: 135 m m = 141 m 17

18 Orders of magnitude Order of magnitude is the power of 10 that applies. Example: John has 3 apples, Jane has 5 apples. Their numbers of apples are of the same order of magnitude Example: 1000 m and 1250 m (10^3) and differ from 1 order of magnitude. 18

19 Coordinate Systems Used to describe the position of a point in space Coordinate system (frame) consists of a fixed reference point called the origin O specific axes with scales and labels (x,y) The direction of the arrow indicate the increasing positive direction. Y Correct Wrong!!!! Y Super Wrong!!!! X 19 X

20 Types of Coordinate Systems Cartesian x- and y- axes points are labeled (x,y) Polar Plane point is distance r from the origin in the direction of angle θ points are labeled (r,θ) θ Anti-clockwise 20