College Physics Chapter 1 Introduction
Theories and Experiments The goal of physics is to develop theories based on experiments A theory is a “guess,” expressed mathematically, about how a system works The theory makes predictions about how a system should work Experiments check the theories’ predictions Every theory is a work in progress
Fundamental Quantities and Their Dimension Length [L] Mass [M] Time [T] other physical quantities can be constructed from these three
Units To communicate the result of a measurement for a quantity, a unit must be defined Defining units allows everyone to relate to the same fundamental amount
Systems of Measurement Standardized systems agreed upon by some authority, usually a governmental body SI -- Systéme International agreed to in 1960 by an international committee main system used in this text also called mks for the first letters in the units of the fundamental quantities
Systems of Measurements, cont cgs – Gaussian system named for the first letters of the units it uses for fundamental quantities US Customary everyday units often uses weight, in pounds, instead of mass as a fundamental quantity
Length Units SI – meter, m cgs – centimeter, cm US Customary – foot, ft Defined in terms of a meter – the distance traveled by light in a vacuum during a given time of 1/ second. This establishes the speed of light at m/sec or its accepted value of 3.00 x 10 8 m/s.
Mass Units SI – kilogram, kg cgs – gram, g USC – slug, slug Defined in terms of kilogram, based on a specific cylinder of platinum and iridium alloy kept at the International Bureau of Weights and Measures located in Sevres, France.
Standard Kilogram
Time Units seconds, s in all three systems times the period of oscillation of radiation from a cesium atom
Approximate Values Various tables in the text show approximate values for length, mass, and time: See Page 3 Note the wide range of values Lengths – Table 1.1 Masses – Table 1.2 Time intervals – Table 1.3
Prefixes Prefixes correspond to powers of 10 Each prefix has a specific name Each prefix has a specific abbreviation See table 1.4 found on page 4 Common prefixes to remember: 10 9 giga, G 10 6 mega, M 10 3 kilo, k 10 1 deka, da deci, d centi, c milli, m micro, nano, n
Structure of Matter Matter is made up of molecules the smallest division that is identifiable as a substance Bodies of mass smaller than the molecule will not have characteristics of a unique substance Molecules are made up of atoms correspond to elements
More structure of matter Atoms are made up of nucleus, very dense, contains protons, positively charged, “heavy” neutrons, no charge, about same mass as protons protons and neutrons are made up of quarks orbited by electrons, negatively charges, “light” fundamental particle, no structure
Structure of Matter
Quarks – up, down, strange, charm, bottom, and top. Up, Charm, and Top have a charge of + that of a proton. Down, Strange, and Bottom have a charge of - that of a proton. The proton has two up quarks and one down quark. + - = + 1. The neutron has two down quarks and one up quark. - - + = 0. The other quarks are indirectly observed and not well understood.
Dimensional Analysis Technique to check the correctness of an equation Dimensions (length, mass, time, combinations) can be treated as algebraic quantities add, subtract, multiply, divide Both sides of equation must have the same dimensions
Dimensional Analysis, cont. Cannot give numerical factors: this is its limitation Dimensions of some common quantities are listed in Table 1.5 on page 5. Example: [a] = [v]/[t]; L/T = {x}/{t 2 } T x = at 2
Uncertainty in Measurements 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
Significant Figures A significant figure is one that is reliably known All non-zero digits are significant Zeros are significant when between other non-zero digits after the decimal point and another significant figure can be clarified by using scientific notation
Operations with Significant Figures Accuracy – number of significant figures When multiplying or dividing two or more quantities, the number of significant figures in the final result is the same as the number of significant figures in the least accurate of the factors being combined
Operations with Significant Figures, cont. When adding or subtracting, round the result to the smallest number of decimal places of any term in the sum If the last digit to be dropped is less than 5, drop the digit If the last digit dropped is greater than or equal to 5, raise the last retained digit by 1
Conversions 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 See the inside of the front cover for an extensive list of conversion factors Example:
Examples of various units measuring a quantity
Order of Magnitude Approximation based on a number of assumptions may need to modify assumptions if more precise results are needed Order of magnitude is the power of 10 that applies Examples: 27~30, ~
Coordinate Systems Used to describe the position of a point in space Coordinate system consists of a fixed reference point called the origin specific axes with scales and labels instructions on how to label a point relative to the origin and the axes
Types of Coordinate Systems Cartesian – (x,y) or (x,y,z) Plane polar- (r,) x y r s
Cartesian coordinate system Also called rectangular coordinate system x- and y- axes Points are labeled (x,y)
Plane polar coordinate system Origin and reference line are noted Point is distance r from the origin in the direction of angle , ccw from reference line Points are labeled (r,)
Trigonometry Review
More Trigonometry Pythagorean Theorem To find an angle, you need the inverse trig function for example, Be sure your calculator is set appropriately for degrees or radians
Problem Solving Strategy
Read the problem Identify the nature of the problem Draw a diagram Some types of problems require very specific types of diagrams
Problem Solving cont. Label the physical quantities Can label on the diagram Use letters that remind you of the quantity Many quantities have specific letters Choose a coordinate system and label it Identify principles and list data Identify the principle involved List the data (given information) Indicate the unknown (what you are looking for)
Problem Solving, cont. Choose equation(s) Based on the principle, choose an equation or set of equations to apply to the problem Substitute into the equation(s) Solve for the unknown quantity Substitute the data into the equation Obtain a result Include units
Problem Solving, final Check the answer Do the units match? Are the units correct for the quantity being found? Does the answer seem reasonable? Check order of magnitude Are signs appropriate and meaningful?
Problem Solving Summary Equations are the tools of physics Understand what the equations mean and how to use them Carry through the algebra as far as possible Substitute numbers at the end Be organized
What is the % uncertainty in the measurement 3.76 0.25? Answer: 0.25/3.76 x 100% = 6.6% What is the % uncertainty in the measurement 11.3 0.9?. Answer: 0.9/11.3 x 100% = 8% Sample Problems
In calculating the area of a piece of notebook paper you get measurements of (21.1 .1) cm for the width and (27.5 .2) cm for the length. Determine the area and the uncertainty. If the actual value of the area is 603 cm 2, determine the percent error from your calculation. Answer: (21.1)(27.5) (21.1)(.2) (25.5)(.1) + (.1)(.2) = 580. ( ) = (580 7) cm 2 % error = (603 – 580) x 100 = 3.8% 603 Sample Problems
An airplane travels at 950 km/h. How long in seconds does it take to travel 1 km? Answer: (950 km/h)(1h/3600sec) =.26sec Use dimensional analysis to determine if the equation v f 2 = v o 2 + 2as is consistent. Answer: [L] 2 = [L] 2 + [L][L] [T] 2 [T] 2 [T] 2 [L] 2 = [L] 2 [T] 2 [T] 2 The equation is consistent. Sample Problems