the science of physics chapter 1 holt. 1.1 what is physics? physics is the scientific study of...

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.

• 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.

http://physics.about.com/od/glossary/g/Matter.htm

http://physics.about.com/od/glossary/g/energy.htm

1.1 Areas Within Physics

Chapter 1Physics 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

length meter m

mass kilogram kg

time second s

temperature Kelvin K

amount of substance mole mol

electric current ampere A

luminous intensity candela cd

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/s2.


Section 2 Measurements in ExperimentsChapter 1

Numbers as Measurements

Chapter 1

Volume

Section 2 Measurements in Experiments

1 dm3 =1 L

1 cm3 = 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.



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.


• SI system– SI system - Current 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 Prefixes– Unit Conversions

• Use the definitions of the metric prefixes to determine correct conversion factors.

1 pm = 10-12 m is an equivalent relationship

To convert m to pm multiply by .

To convert pm to m multiply by .

1 pm10-12 m

10-12 m1pm

http://physics.nist.gov/cuu/Units/current.html

http://www.essex1.com/people/speer/large.html


• 6 003 000 pm = _________ m

6 003 000 pm x 10-12 m

1pm = 6.003 x 10-6 m

• Convert 73.5 km/h to its equivalent in m/s.

Know: 1000m = 1km; 60s = 1 min; 60 min = 1h

mkm

kmh

1 h60 min

1 min60 s

= 20.41666666667 m/s = 20.4 m/s

73.5 x 1000 xx

Unit Conversions

• p. 15 #1-5

• Convert 60,500 cm3 to m3.

• Convert 55 mi/h to km/h (1.6 km = 1 mi).

1. 50 mm x 1 m/1 000 000 mm = 5.0 x 10-5 m

2. 1 ms x 1 s/1 000 000 ms = 1.0 x 10-6 s

3. a. 10 nm x 10-9 m/nm = 1.0 x 10-8 m

b. 1.0 x 10-8 m x 1 000 mm/m = 1.0 x 10-5 mm

c. 1.0 x 10-8 m x 1x106 mm/m = 1.0 x 10-2 mm

4. 1.5 x 1011 m = 150 Gm = 0.15 Tm = 1.5 x 108 km

5. 1.440 x 103 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.



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 cm0cm

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 = 0.72 + 0.01 cm



Rectangle

a

b

1.0 cm0cm

Side a is about 0.50 cm.

a = 0.49 + 0.01 cm




a

b

1.0 cm0

What is the range of uncertainty in the area of the rectangle?

Extremes:

A = 0.71 cm x 0.48 cm = 0.3408 cm2

A = 0.73 cm x 0.50 cm = 0.3650 cm2

The true area is somewhere between 0.3408 cm2 and 0.3650 cm2.

Average measured values of 0.72 cm and 0.49 cm give an area of 0.3528 cm2. A good approximation of the area is 0.35 + 0.01 cm2 or just 0.35 cm2.

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.



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.

http://scidiv.bcc.ctc.edu/Physics/measure&sigfigs/B-Acc-Prec-Unc.html


• 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?

Student Group

Student 1 Student 2 Student 3 Student 4 Student 5

Group A 10.1 10.4 9.6 9.9 10.8

Group B 10.135 10.227 10.201 10.011 10.155

Group C 12.14 12.17 12.15 12.14 12.18

Group D 10.05 10.82 8.01 11.5 10.77

Group E 10 11 10 10 10

Unknown

C

Unknown

D

10.2

10.146

12.16

10.23

10

Average Scatter

1.2

.216

0.03

3.49

1


• 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 = 10.160 cm)


Student Group

Student 1 Student 2 Student 3 Student 4 Student 5

Group A 10.1 10.4 9.6 9.9 10.8

Group B 10.135 10.227 10.201 10.011 10.155

Group C 12.14 12.17 12.15 12.14 12.18

Group D 10.05 10.82 8.01 11.5 10.77

Group E 10 11 10 10 10

• 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 = 10.160 cm)


• 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 ExperimentsSignificant 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. 62.5 34.996

– Any zeros between two significant digits are significant. 3042 0040.003 040

– A final zero or trailing zeros in the decimal portion ONLY are significant.

3 2003.20 x 103

204.06110

3 s.f.5 s.f.

3 s.f.4 s.f.

4 s.f.

8 s.f.

3 s.f.

2 s.f.


• Significant Figures

What is the precision for each of the following measurements? How many significant figures are in each measurement?

a) 62.5 m tenths place 3 s.f. b) 34.996 m thousandths of a meter 5 s.f.c) 304 m one meter 3 s.f.d) 0.003 040 m millionth of a meter 4 s.f.e) 1 200 m nearest 100 meter 2 s.f.f) 3.20 x 103 m nearest 10 meter 3 s.f.g) 204.061 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


Scientific Notation

Scientific notation shows only the significant figures.

202000 = 2.02 x 105

0.00001023900 = 1.023900 x 10-5

1.2 Measurements in Experiments• Answers obtained from calculations must be rounded to indicate the

correct number of significant figures.

Rule Example

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.

56.87 g --> 56.9 g

12.02 L --> 12.0 L

3.7851 --> 3.79

2.835 s --> 2.84 s

2.650 mL --> 2.6 mL


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 + 2.03 g = 27.13 g

Answer: 27.1 g• EX: 126 cm + 9.45 cm = 135.45 cm

Answer: 135 cm


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 = 0.360094451 g /mL

Answer: 0.360 g/mL

Conversion Factors do not limit the number of significant figures shown in the final answer


• 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.

• http://shazam.econ.ubc.ca/intro/round.htm

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 1Section 3 The Language of Physics

Inverse Square Relationship y = k(1/x2)

Inverse Proportion

y = k(1/x)

Interpreting Graphs

Chapter 1Section 3 The Language of Physics

y varies with x2

y = ax2

• the time a SCUBA tank lasts at various pressures

• Graphs


t = k/p

y = kx2

• 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.


distance/time x distance = distance2/time = time

240 km x 80 km/h

240 km x h/80 km = 3 h


Practice 1. E = mc2 What are the units for c if E is kg.m2/s2 and

m is kg?

2. In what units would a be reported? vf and vo have units of m/s

a = (vf - vo)/Dt

3. If a is acceleration (m/s2 ), Dv is change in velocity (m/s), Dx is change in position (m), and Dt is the time interval (s), which equation is dimensionally correct?

a. Dt = Dx ¤v b. a = v ¤Dx c. Dv = a ¤Dt d. Dt = Dx2 ¤a

• p. 25 1, 2, 4, and 5


• p. 25 2

a. kg. m/s2

b. kg. m/s3

c. kg .m2/s3

d. kg.m/s2


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