The Science of Physics Chapter 1 Holt

1.1 What Is Physics? Physics is the scientific study of matter and energy and how they interact with each other.matter energy This energy can take the form of motion, light, electricity, radiation, gravity... Physics deals with matter on scales ranging from sub-atomic particles to stars and even entire galaxies. The goal of physics is to use a small number of basic concepts, equations, and assumptions to describe the physical world.

1.1 Areas Within Physics

Chapter 1 Physics and Technology Section 1 What Is Physics?

1.1 What Is Physics? The scientific method is a logical approach to solving problems. A set of particles or interacting components considered to be a distinct physical entity for the purpose of study is called a system. A hypothesis is an explanation based on prior scientific research or observations that can be tested. A hypothesis is not a question. The process of simplifying and modeling a situation can help you determine the relevant variables and identify a hypothesis for testing.

Numbers as Measurements Measurements have a number and a unit! Never assume the unit is understood; always write the unit. The unit tells us two things about a number: 1)Dimension or quantity measured, such as length, mass, time, temperature, … 2) How much of the quantity is represented, such as kilometer, meter, centimeter, millimeter, nanometer … 1.2 Measurements in Experiments

Quantity Unit Abbreviation lengthmeter m masskilogram kg timesecond s temperatureKelvin K amount of substance mole mol electric currentampereA luminous intensitycandelacd 7 SI Base Units Each base unit describes a single dimension, such as length, mass, or time.

SI Standards Derived units are formed by combining the seven base units with multiplication or division. Units for velocity, force, momentum, energy, volume, and acceleration are derived from these three base units. For example, 1 Newton = 1 kg. m/s Measurements in Experiments

Section 2 Measurements in Experiments Chapter 1 Numbers as Measurements

Chapter 1 Volume Section 2 Measurements in Experiments 1 dm 3 =1 L 1 cm 3 = 1 mL = 1 cc

SI Prefixes In SI, units are combined with prefixes that symbolize certain powers of 10. The most common prefixes and their symbols are shown in the table. 1.2 Measurements in Experiments

Dimensions and Units Measurements of physical quantities must be expressed in units that match the dimensions of that quantity. (Length is measured in meters not grams.) In addition to having the correct dimension, measurements used in calculations should have the same units. Convert so that units are the same. For example, when determining area by multiplying length and width, be sure the measurements are expressed in the same units.

1.2 Measurements in Experiments SI system –SI system - Current definitions of the SI unitsCurrent definitions of the SI units –Metric System Prefixes: Unit symbols are written as normal letters, i.e. not italicized or boldfaced.) –Large and Small Numbers - Metric PrefixesLarge and Small Numbers - Metric Prefixes –Unit Conversions Use the definitions of the metric prefixes to determine correct conversion factors. 1 pm = m is an equivalent relationship To convert m to pm multiply by. To convert pm to m multiply by. 1 pm m 1pm

1.2 Measurements in Experiments pm = _________ m pm x m 1pm = x m Convert 73.5 km/h to its equivalent in m/s. Know: 1000m = 1km; 60s = 1 min; 60 min = 1h m km h 1 h 60 min 1 min 60 s = m/s = 20.4 m/s 73.5x 1000 xx Unit Conversions

p. 15 #1-5 Convert 60,500 cm 3 to m 3. Convert 55 mi/h to km/h (1.6 km = 1 mi)  m x 1 m/  m = 5.0 x m 2.1  s x 1 s/  s = 1.0 x s 3.a. 10 nm x m/nm = 1.0 x m b. 1.0 x m x mm/m = 1.0 x mm c. 1.0 x m x 1x10 6  m/m = 1.0 x  m x m = 150 Gm = 0.15 Tm = 1.5 x 10 8 km x 10 3 kg 1.2 Measurements in Experiments

Accuracy and Precision –Accuracy refers to the agreement between a measurement and the true or correct value. Errors in measurement affect accuracy. –Precision refers to the repeatability of measurement. It is the degree of exactness of a set of measurements and is limited by the finest division on the measuring instrument scale.

Error (or percent error reported in lab write-ups) refers to the disagreement between a measurement and the true or accepted value. A numeric measure of confidence in a measurement or result is known as uncertainty. A lower uncertainty indicates greater confidence. Uncertainty of a measured value is an interval around that value such that any repetition of the measurement will produce a new result that lies within this interval. 1.2 Measurements in Experiments

Rectangle a b Determine the area of the rectangle. What would you do?

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Rectangle a b 1.0 cm 0 cm 1.2 Uncertainty in Measurement Side b is about 0.72 cm. Estimate possible error in reading the ruler is 0.01 cm. (Uncertainty is 0.01 cm) Correct reading is between 0.71 and 0.73 cm b = cm

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Rectangle a b 1.0 cm 0 cm Side a is about 0.50 cm. a = cm 1.2 Uncertainty in Measurement

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu a b 1.0 cm 0 What is the range of uncertainty in the area of the rectangle? Extremes: A = 0.71 cm x 0.48 cm = cm 2 A = 0.73 cm x 0.50 cm = cm 2 The true area is somewhere between cm 2 and cm 2. Average measured values of 0.72 cm and 0.49 cm give an area of cm 2. A good approximation of the area is cm 2 or just 0.35 cm 2. To report to the ten thousandths place indicates that you measured to the nearest ten thousandths cm. In our case the third and fourth decimal places have no meaning. 1.2 Uncertainty in Measurement

1.2 Measurements in Experiments A metal rod about 4 inches long has been passed around to several groups of students. Each group is asked to measure the length of the rod. Each group has five students and each student independently measures the rod and records his or her result.

1.2 Measurements in Experiments Which group has the most accurate measurement? Which group has the most precise measurement? Which group has the greatest error? Which group has the greatest uncertainty? Unknown C D AverageScatter

1.2 Measurements in Experiments We now receive a report from the machine shop where the rod was manufactured. This very reputable firm certifies the rod to be 4 inches long to the nearest thousandths of an inch. Answer the questions below given this new information. Note that the questions are slightly different. (4.000 inches = cm)

1.2 Measurements in Experiments Which group has the least accurate measurement? Which group has the least precise measurement? Which group has the smallest error? Which group has the smallest uncertainty? C D A (Average is closest to accepted value.) C (4.000 inches = cm)

1.2 Measurements in Experiments Significant Figures –It is important to record the precision of your measurements so that other people can understand and interpret your results. –A common convention used in science to indicate precision is known as significant figures. –Significant figures are those digits in a measurement that are known with certainty plus the first digit that is uncertain.

1.2 Measurements in Experiments Significant Figures Even though this ruler is marked in only centimeters and half- centimeters, you can estimate and use it to report measurements to a precision of a millimeter (1/10 of a centimeter).

1.2 Measurements in Experiments Significant Figures –Non-zero digits are always significant –Any zeros between two significant digits are significant –A final zero or trailing zeros in the decimal portion ONLY are significant x s.f. 5 s.f. 3 s.f. 4 s.f. 8 s.f. 3 s.f. 2 s.f.

1.2 Measurements in Experiments Significant Figures What is the precision for each of the following measurements? How many significant figures are in each measurement? a)62.5 mtenths place 3 s.f. b) m thousandths of a meter 5 s.f. c)304 m one meter 3 s.f. d) m millionth of a meter 4 s.f. e)1 200 m nearest 100 meter 2 s.f. f)3.20 x 10 3 m nearest 10 meter 3 s.f. g) m hundred thousandths of a meter, 6 s.f. Which measurement(s) has the greatest uncertainty? e Which measurement(s) has the least precision? e Which measurement(s) has the greatest precision? d

1.2 Measurements in Experiments Scientific Notation Scientific Notation Scientific notation shows only the significant figures = 2.02 x = x 10 -5

1.2 Measurements in Experiments Answers obtained from calculations must be rounded to indicate the correct number of significant figures. RuleExample If the digit immediately to the right of the last significant figure you want to retain is Greater than 5, increase the last digit by 1. Less than 5, do not change the last digit. 5, followed by nonzero digit(s), increase the last digit by 1. 5, not followed by a nonzero digit and preceded by odd digit(s), increase the last digit by 1. 5, not followed by nonzero digit(s), and the preceding significant digit is even, do not change the last digit g --> 56.9 g L --> 12.0 L > s --> 2.84 s mL --> 2.6 mL

1.2 Measurements in Experiments Rounding Addition/Subtraction: : The answer must have its last significant figure in the same decimal place as the measurement with the most uncertainty. EX: 25.1 g g = g Answer: 27.1 g EX: 126 cm cm = cm Answer: 135 cm

1.2 Measurements in Experiments Multiplication/Division: the answer can have no more significant figures than are in the measurement with the fewest number of significant figures Ex: Calculating density D = 3.05 g / 8.47 mL D = g /mL Answer: g/mL Conversion Factors do not limit the number of significant figures shown in the final answer

1.2 Measurements in Experiments You will often use the results of one calculation as one of the values in a subsequent calculation. That answer may then be used in yet another calculation and so on. Repeated rounding at each step can introduce errors that would not occur if you combined all of the steps algebraically and computed the final result all at once.

Practice p. 20 1, 3, and 4

Mathematics and Physics Tables, graphs, and equations can make data easier to understand. –In this experiment, a table-tennis ball and a golf ball are dropped in a vacuum. 1.3 The Language of Physics Trends??

Data from Dropped-Ball Experiment A clear trend can be seen in the data. The more time that passes after each ball is dropped, the farther the ball falls.

Graph from Dropped-Ball Experiment One method for analyzing the data is to construct a graph of the distance the balls have fallen versus the elapsed time since they were released. The shape of the graph provides information about the relationship between time and distance.

Interpreting Graphs Chapter 1:3 The Language of Physics Linear Relationship y = mx + b Direct Proportion y = mx

Interpreting Graphs Chapter 1 Section 3 The Language of Physics Inverse Square Relationship y = k(1/x 2 ) Inverse Proportion y = k(1/x)

Interpreting Graphs Chapter 1 Section 3 The Language of Physics y varies with x 2 y = ax 2

the time a SCUBA tank lasts at various pressures Graphs 1.3 The Language of Physics t = k/p y = kx 2

Dimensional analysis can weed out invalid equations. (Watch your units!) –Calculate the time is will take a person to travel 240 km if their average speed is 80 km/h. 1.3 The Language of Physics distance/time x distance = distance 2 /time = time 240 km x 80 km/h 240 km x h/80 km = 3 h

1.3 The Language of Physics Practice 1. E = mc 2 What are the units for c if E is kg. m 2 /s 2 and m is kg? 2. In what units would a be reported? v f and v o have units of m/s a = (v f - v o )/  t 3. If a is acceleration (m/s 2 ),  v is change in velocity (m/s),  x is change in position (m), and  t is the time interval (s), which equation is dimensionally correct? a.  t =  x  v b. a = v  x c.  v = a  t d.  t =  x 2  a

p. 25 1, 2, 4, and The Language of Physics

p a.kg. m/s 2 b.kg. m/s 3 c.kg. m 2 /s 3 d.kg. m/s The Language of Physics