Principles and Problems - Weebly · • Physicists often use the language of mathematics. • Physicists rely on theories and experiments with numerical results to support their conclusions.

Chapter 1: A Physics Toolkit

PHYSICSPrinciples and Problems

BIG IDEA

Physicists use scientific methods to investigate

energy and matter.

CHAPTER

1 A Physics Toolkit

Section 1.1 Methods of Science

Section 1.2 Mathematics and Physics

Section 1.3 Measurement

Section 1.4 Graphing Data

CHAPTER

1 Table Of Contents

Click a hyperlink to view the corresponding slides. Exit

Essential Questions

• What are the characteristics of scientific methods?

• Why do scientists use models?

• What is the difference between a scientific theory and

a scientific law?

• What are some limitations of science?

MAIN IDEA

Scientific investigations do not always proceed with

identical steps but do contain similar methods.

SECTION

1.1 Methods of Science

New Vocabulary

• Physics

• Scientific methods

• Hypothesis

Review Vocabulary

• Control the standard by which test results in an

experiment can be compared.

• Model

• Scientific theory

• Scientific law

SECTION

Physics is a branch of science that involves the

study of the physical world: energy, matter, and

how they are related.

Learning physics will help you to understand

the physical world.

What is Physics?

SECTION

• Although physicists do not

always follow a rigid set of

steps, investigations often

follow similar patterns called

scientific methods.

• Depending on the particular

investigation, a scientist might

add new steps, repeat some

steps or skip steps altogether.

Scientific Methods

SECTION

• Many investigations begin when someone

observes an event in nature and wonders why or

how it occurs.

• The question of “why” or “how” is the problem.

– Many questions have been asked throughout history:

why objects fall to Earth, what causes day and night,

how to generate electricity…

– Often the investigation into one problem may lead to

more questions and more investigations.

Scientific Methods (cont.)

SECTION

• Researching already known information about a

problem, helps to fine-tune the question and

form it into a hypothesis.

– Hypothesis is a possible explanation for a problem

using what you know and have observed.

SECTION

• Hypotheses can be tested by different means:

– Observations

– Models

– Experiments

• Test the effect of one thing on another, using a control.

SECTION

• An important part of every investigation includes recording observations and organizing data into easy-to-read tables and graphs.

• Based on the analysis of the data, the next step is to decide whether the hypothesis is supported.

– If supported, the data must be reproducible many times.

– If not supported, the hypothesis must be reconsidered.

SECTION

• Sometimes, scientists cannot see everything they

are testing. They might be observing an object

that is too large or too small, a process that takes

too much time to see completely, or a material that

is hazardous.

• A model is a representation of an idea, event,

structure, or object that helps people better

understand it.

Models

SECTION

• A scientific theory is an explanation of things or

events based on knowledge gained from many

observations and investigations.

– This is not a hypothesis, this is what a hypothesis

becomes after numerous trials of data supporting the

hypothesis.

– A theory is never permanent, it can change as new data

and information becomes available.

Scientific Theories and Laws

SECTION

• A scientific law is a statement about what

happens in nature and seems to be true all the

– Laws tell you what will happen under certain conditions,

but they do not explain why or how something happens.

Ex. Gravity

• The law of gravity states that any one mass will attract another

• There are many theories proposed to explain how the law of

gravity works.

Scientific Theories and Laws (cont.)

SECTION

• Science cannot explain or solve every question.

• A scientific question must be testable and

verifiable.

– Questions about opinions, values or emotions are not

scientific because they cannot be tested.

The Limitations of Science

SECTION

The similar patterns used, by all branches of

science, in an investigation are called?

A. Hypotheses

B. Scientific theories

C. Scientific methods

D. Scientific laws

SECTION

1.1 Section Check

“In a closed-system, mass is always

conserved” is an example of which of the

following?

A. Scientific law

B. Scientific theory

C. Hypothesis

D. Model

SECTION

1.1 Section Check

MAIN IDEA

We use math to express concepts in physics.

Essential Questions

• Why do scientists use the metric system?

• How can dimensional analysis help evaluate answers?

• What are significant figures?

SECTION

1.2 Mathematics and Physics

Review Vocabulary

• SI International System of Units – the improved,

universally accepted version of the metric system that

is based on multiples of ten.

New Vocabulary

• Dimensional analysis

• Significant figures

SECTION

• Physicists often use the language of mathematics.

• Physicists rely on theories and experiments with

numerical results to support their conclusions.

Mathematics in Physics

SECTION

• In order to communicate

results that everyone can

understand, the worldwide

scientific community uses

an adaptation of the metric

system called Systeme

International d’Unites or SI.

• The SI system of

measurement uses seven

base quantities.

SI Units

SECTION

• The base quantities were originally defined in terms of

direct measurements. Other units, called derived units, are

created by combining the base units in various ways.

• The SI system is regulated by the International Bureau of

Weights and Measures in Sèvres, France.

• This bureau and the National Institute of Science and

Technology (NIST) in Gaithersburg, Maryland, keep the

standards of length, time, and mass against which our

metersticks, clocks, and balances are calibrated.

SI Units (cont.)

SECTION

• Another feature in the SI

system is the ease of

converting units.

• To convert between

units, multiply or divide

by the appropriate power

of 10.

• Prefixes are used to

change SI base units to

powers of 10.

SECTION

SI Units (cont.)

Dimensional Analysis

• You will often need to use different versions of a

formula, or use a string of formulas, to solve a

physics problem.

• To check that you have set up a problem correctly,

write the equation or set of equations you plan to

use with the appropriate units.

SECTION

• Before performing calculations, check that the

answer will be in the expected units.

• For example, if you are finding a speed and you see

that your answer will be measured in s/m, you know

you have made an error in setting up the problem.

• This method of treating the units as algebraic

quantities, which can be cancelled, is called

dimensional analysis.

Dimensional Analysis (cont.)

SECTION

• Dimensional analysis is also used in choosing

conversion factors.

• A conversion factor is a multiplier equal to 1. For

example, because 1 kg = 1000 g, you can

construct the following conversion factors:

SECTION

• Choose a conversion factor that will make the units

cancel, leaving the answer in the correct units.

• For example, to convert 1.34 kg of iron ore to

grams, do as shown below:

SECTION

• A meterstick is used to measure a pen and you find the end

of the pen is in between 138 and 139mm. You estimate

that the pen is two-tenths of a millimeter past the 138 mark

and record the measurement as 138.2mm.

• This measurement has four valid digits: three you are sure

of, and one you estimated.

• The valid digits in a measurement are called significant

figures.

• However, the last digit given for any measurement is the

uncertain digit.

SECTION

Significant Figures

Significant Figures (cont.)

• All nonzero digits in a measurement are

significant, but not all zeros are significant.

• Consider a measurement such as 0.0860 m. Here

the first two zeros serve only to locate the decimal

point and are not significant.

• The last zero, however, is the estimated digit and

is significant.

SECTION

• When you perform any arithmetic operation, it is

important to remember that the result can never be

more precise than the least-precise measurement.

• To add or subtract measurements:

–First perform the operation, then round off the result to

correspond to the least-precise value involved. Ex.

3.86m + 2.4m = 6.3m

SECTION

• To multiply or divide measurements:

–Perform the calculation and then round to the same

number of significant digits as the least-precise

measurement. Ex. 409.2km/11.4L = 35.9km/L

• Note: Significant digits are considered only when

calculating with measurements. There is no

uncertainty associated with counting (4 washers)

or exact conversion factors (24 hours in 1 day).

SECTION

The potential energy, PE, of a body of mass, m, raised

to a height, h, is expressed mathematically as PE = mgh,

where g is the gravitational constant. If m is measured

in kg, g in m/s2, h in m, and PE in joules, then what is 1

joule described in base units?

SECTION

1.2 Section Check

A. 1 kg·m/s

B. 1 kg·m/s2

C. 1 kg·m2/s

D. 1 kg·m2/s2

Answer

Reason:

SECTION

1.2 Section Check

A car is moving at a speed of 90 km/h. What is

the speed of the car in m/s? (Hint: Use

Dimensional Analysis)

SECTION

1.2 Section Check

A. 2.5×101 m/s

B. 1.5×103 m/s

C. 2.5 m/s

D. 1.5×102 m/s

Answer

Reason:

SECTION

1.2 Section Check

Which of the following representations is correct

when you solve 0.030 kg + 3333 g using

scientific notation?

SECTION

1.2 Section Check

A. 3.4×103 g (Wrong Answer!)

B. 3.36×103 g

C. 3×103 g

D. 3.363×103 g (this is correct)

Answer

Reason: 0.030 kg is the same as 30.g –

significant to the one’s place.

3333 has four significant digits – alao

significant to the one’s place.

Therefore, our answer should contain 4

significant digits to the one’s place.

SECTION

1.2 Section Check

MAIN IDEA

Making careful measurements allows scientists to repeat

experiments and compare results.

Essential Questions

• Why are the results of measurements often reported

with an uncertainty?

• What is the difference between precision and

accuracy?

• What is a common source of error when making a

measurement?

SECTION

1.3 Measurement

Review Vocabulary

• Parallax the apparent shift in the position of an object

when it is viewed from different angles.

New Vocabulary

• Measurement

• Precision

• Accuracy

SECTION

1.3 Measurement

• A measurement is a comparison between an

unknown quantity and a standard.

–Ex. Measuring the mass of a rolling cart. The

unknown quantity is the cart, the standard is the gram

as defined the instrument being used.

• Measurements quantify observations.

• Careful measurements enable you to derive the

relationship between any two quantities.

What is a Measurement?

SECTION

1.3 Measurement

• When a measurement is made, the results are

often reported with uncertainty.

• Therefore, before fully accepting new data, other

scientists examine the experiment, looking for

possible sources of errors, and try to reproduce

the results.

• A new measurement that is within the margin of

uncertainty confirms the old measurement.

Comparing Results

SECTION

1.3 Measurement

Precision Versus Accuracy

Click image to view the movie.

SECTION

1.3 Measurement

• To assure precision and accuracy, instruments

used to make measurements need to be used

correctly.

• This is important because one common source of

error comes from the angle at which an instrument

is read.

Techniques of Good Measurement

SECTION

1.3 Measurement

• Scales should be read with one’s

eye straight in front of the measure.

• If the scale is read from an angle,

as shown in figure (b), you will get

a different, and less accurate,

value.

Techniques of Good Measurement

• The difference in readings is

caused by parallax, which is

the apparent shift in the position of an object when it is

viewed from different angles.

SECTION

1.3 Measurement

Ronald, Kevin, and Paul perform an experiment to determine

the value of acceleration due to gravity on Earth (which most

scientists agree is about 980 cm/s2). The following results

were obtained: Ronald — 961 ± 12 cm/s2, Kevin — 953 ± 8

cm/s2, and Paul — 942 ± 4 cm/s2. Determine who has the

most accurate and precise value.

A. Kevin got the most precise and accurate value.

B. Ronald’s value is the most accurate, while Kevin’s value is the

most precise.

C. Ronald’s value is the most accurate, while Paul’s value is the

most precise.

D. Paul’s value is the most accurate, while Ronald’s value is the

most precise.

SECTION

1.3 Measurement

Answer

Reason: Ronald’s answer is closest to 980 cm/s2.

Hence, Ronald’s result is the most

accurate. However, Paul’s error is only ±4

cm/s2. Hence, Paul’s result is the most

precise.

SECTION

1.3 Section Check

What is the precision of an instrument?

A. the smallest divisions marked on the instrument

B. the least count written on the instrument

C. one-half the least count written on the instrument

D. one-half the smallest division written on the

instrument

SECTION

1.3 Section Check

Answer

Reason: Precision depends on the instrument and

the technique used to make the

measurement. Generally, the device with

the finest division on its scale produces

the most precise measurement. The

precision of a measurement is one-half of

the smallest division of the instrument.

SECTION

1.3 Section Check

A 100-cm long rope was measured with three different

measuring tapes. The answer obtained with the three

measuring tapes were: 1st measuring tape — 99 ± 0.5 cm,

2nd measuring tape — 98 ± 0.25 cm, and 3rd measuring

tape — 99 ± 1 cm. Which measuring tape is the most

precise?

A. 1st measuring tape

B. 2nd measuring tape

C. 3rd measuring tape

D. Both measuring tapes 1 and 3

SECTION

1.3 Section Check

Answer

Reason: Precision depends on the instrument. The

2nd measuring tape has an error of only

±0.25 cm and is therefore the most

precise.

SECTION

1.3 Section Check

MAIN IDEA

Graphs make it easier to interpret data, identify trends and

show relationships among a set of variables.

Essential Questions

• What can be learned from graphs?

• What are some common relationships in graphs?

• How do scientists make predictions?

SECTION

1.4 Graphing Data

Review Vocabulary

• Slope on a graph, the ratio of vertical change to

horizontal change.

New Vocabulary

• Independent variable

• Dependent variable

• Line of best fit

• Linear relationship

• Quadratic relationship

• Inverse relationship

SECTION

1.4 Graphing Data

• A variable is any factor that might affect the

behavior of an experimental setup.

• The independent variable is the factor that is

changed or manipulated during the experiment.

• The dependent variable is the factor that

depends on the independent variable.

Identifying Variables

SECTION

1.4 Graphing Data

Click image to view the movie.

Identifying Variables (cont.)

SECTION

1.4 Graphing Data

• Scatter plots of data may take many different

shapes, suggesting different relationships.

• Three of the most common relationships include

linear relationships, quadratic relationships and

inverse relationships.

Linear Relationships

SECTION

1.4 Graphing Data

• When the line of best fit is a

straight line, as in the figure,

the dependent variable varies

linearly with the independent

variable. This relationship

between the two variables is

called a linear relationship.

• The relationship can be written

as an equation.

SECTION

1.4 Graphing Data

• The slope is the ratio of the vertical change to the horizontal change. To find the slope, select two points, A and B, far apart on the line. The vertical change, or rise, Δy, is the difference between the vertical values of A and B. The horizontal change, or run, Δx, is the difference between the horizontal values of A and B.

SECTION

1.4 Graphing Data

• As presented in the previous slide, the slope of a line is

equal to the rise divided by the run, which also can be

expressed as the change in y divided by the change in x.

• If y gets smaller as x gets larger, then Δy/Δx is negative,

and the line slopes downward.

• The y-intercept, b, is the point at which the line crosses the

y-axis, and it is the y-value when the value of x is zero.

SECTION

1.4 Graphing Data

• When the graph is not a straight line, it means that

the relationship between the dependent variable

and the independent variable is not linear.

• There are many types of nonlinear relationships in

science. Two of the most common are the

quadratic and inverse relationships.

Nonlinear Relationships

SECTION

1.4 Graphing Data

• The graph shown in the

figure is a quadratic

relationship.

• A quadratic

relationship exists when

one variable depends on

the square of another.

SECTION

1.4 Graphing Data

• A quadratic relationship can be represented by the

following equation:

SECTION

1.4 Graphing Data

• The graph in the figure shows

how the current in an electric

circuit varies as the resistance is

increased. This is an example of

an inverse relationship.

• In an inverse relationship, a

hyperbola results when one

variable depends on the inverse

of the other.

SECTION

1.4 Graphing Data

• An inverse relationship can be represented by the

following equation:

SECTION

1.4 Graphing Data

• There are various mathematical models available

apart from the three relationships you have

learned. Examples include sinusoids, which are

used to model cyclical phenomena, and

exponential decay curves, which are used to

model radioactivity.

• Combinations of different mathematical models

represent even more complex phenomena.

SECTION

1.4 Graphing Data

• Relations, either learned as formulas or developed

from graphs, can be used to predict values you have

not measured directly.

• Physicists use models to accurately predict how

systems will behave: what circumstances might lead

to a solar flare, how changes to a circuit will change

the performance of a device, or how electromagnetic

fields will affect a medical instrument.

Predicting Values

SECTION

1.4 Graphing Data

Which type of relationship is shown by the

following graph?

A. Linear

B. Inverse

C. Parabolic

D. Quadratic

SECTION

1.4 Section Check

Answer

Reason: In an inverse relationship, a hyperbola

results when one variable depends on the

inverse of the other.

SECTION

1.4 Section Check

What is a line of best fit?

A. the line joining the first and last data points in a graph

B. the line joining the two center-most data points in a

C. the line drawn as close to all the data points as

possible

D. the line joining the maximum data points in a graph

SECTION

1.4 Section Check

Answer

Reason: The line drawn closest to all data points as

possible is called the line of best fit. The

line of best fit is a better model for

predictions than any one or two points that

help to determine the line.

SECTION

1.4 Section Check

Which relationship can be written as y = mx + b?

A. Linear relationship

B. Quadratic relationship

C. Parabolic relationship

D. Inverse relationship

SECTION

1.4 Section Check

Answer

Reason: A linear relationship can be written as y =

mx + b, where m is the slope and b is the

y-intercept.

SECTION

1.4 Section Check

Physics Online

Study Guide

Chapter Assessment Questions

Standardized Test Practice

A Physics ToolkitCHAPTER

Resources

• Scientific methods include making observations and

asking questions about the natural world.

• Scientists use models to represent things that may be

too small or too large, processes that take too much

time to see completely, or a material that is

hazardous.

Methods of ScienceSECTION

Study Guide

• A scientific theory is an explanation of things or

events based on knowledge gained from

observations and investigations. A scientific law is a

statement about what happens in nature, which

seems to be true all the time.

• Science can not explain or solve everything.

Questions about opinions or values can not be

tested.

Methods of ScienceSECTION

Study Guide

• Using the metric system helps scientists around the

world communicate more easily.

• Dimensional analysis is used to check that an answer

will be in the correct units.

• Significant figures are the valid digits in a

measurement.

Mathematics and PhysicsSECTION

Study Guide

• Measurements are reported with uncertainty because a

new measurement that is within the margin of

uncertainty confirms the old measurement.

• Precision is the degree of exactness with which a

quantity is measured. Accuracy is the extent to which a

measurement matches the true value.

• A common source of error that occurs when making a

measurement is the angle at which an instrument is

read. If the scale of an instrument is read an angle, as

opposed to eye level, the measurement will be less

accurate.

MeasurementSECTION

Study Guide

• Graphs contain information about the relationships

among variables. Patterns that are not immediately

evident in a list of numbers are seen more easily when

the data are graphed.

Graphing DataSECTION

Study Guide

• Common relationships shown in graphs include linear

relationships, quadratic relationships and inverse

relationships. In a linear relationship, the dependent

variable varies linearly with the independent variable. A

quadratic relationship occurs when one variable

depends on the square of an another. In an inverse

relationship, one variable depends on the inverse of the

other variable.

• Scientists use models and relationships between

variables to make predictions.

Graphing DataSECTION

Study Guide

How will you express 1 nm in m?

A. 1×10-3 m

B. 1×10-6 m

C. 1×10-9 m

D. 1×10-1 m

Chapter Assessment

Reason: 1 nm is read as 1 nanometer. The prefix

nano stands for 10-9.

Chapter Assessment

Add the following numbers and write the

answer using the proper number of significant

digits: 12.3 + 1.2 + 123.

A. 136.5

B. 1.4 × 102

C. 137

D. 1.37 × 102

Chapter Assessment

Reason: The last digit in 12.3 and 1.2 are both

in the tenth’s place. However, the last

digit in 123 is in the one’s place.

Therefore, the last digit of the answer

should be in the one’s place.

Chapter Assessment

Rewrite 3.650 with only 2 significant digits.

A. 3.7

B. 3.6

C. 3.65

D. 0.360 × 101

Chapter Assessment

Reason: The last reported digit would be the 6.

The digit to the right is a 5 followed

by a zero. Therefore since the 6 is

even it remains so and the answer

would be 3.6.

Chapter Assessment

If 15 different individuals perform an experiment, and

15 answers are obtained, which answer will be

accepted as the most accurate?

A. the answer obtained by the highest number of persons

B. the eighth number if all the numbers are arranged in an

ascending order

C. the answer nearest to the expected answer

D. the average of all 15 answers

Chapter Assessment

Reason: Accuracy describes how well the result

of a measurement agrees with the

expected value.

Chapter Assessment

A quadratic relationship between two variables

is written as ____.

Chapter Assessment

Reason: A quadratic relationship between two

variables is written as

y = ax2 + bx + c.

Chapter Assessment

Two laboratories use radiocarbon dating to measure the

age of two wooden spear handles found in the same

grave. Lab A finds an age of 2250 40 years for the first

object; lab B finds an age of 2215 50 years for the

second object. Which of the following is true?

A. Lab A’s reading is more accurate than lab B’s.

B. Lab A’s reading is less accurate than lab B’s.

C. Lab A’s reading is more precise than lab B’s.

D. Lab A’s reading is less precise than lab B’s.

Which of the following is equal to 86.2 cm?

A. 8.62 m

B. 0.862 mm

C. 8.62×10-4 km

D. 862 dm

Jario has a homework problem to do involving time,

distance, and velocity, but he has forgotten the formula.

The question asks him for a measurement in seconds,

and the numbers that are given have units of m/s and km.

What could Jario do to get the answer in seconds?

A. Multiply the km by the m/s, then multiply by 1000.

B. Divide the km by the m/s, then multiply by 1000.

C. Divide the km by the m/s, then divide by 1000.

D. Multiply the km by the m/s, then divide by 1000.

What is the slope of the graph?

A. 0.25 m/s2

B. 0.4 m/s2

C. 2.5 m/s2

D. 4.0 m/s2

Which formula is equivalent to

Skip Around if You Can

You may want to skip over difficult questions and

come back to them later, after you’ve answered

the easier questions. This will guarantee more

points toward your final score. In fact, other

questions may help you answer the ones you

skipped. Just be sure you fill in the correct ovals

on your answer sheet.

Test-Taking Tip

Length of a Spring for Different Masses (1)

Chapter Resources

Length of a Spring for Different Masses (2)

Chapter Resources

Graph Indicating a Quadratic, or Parabolic,

Relationship

Chapter Resources

Graph Showing the Inverse Relationship

Between Resistance and Current

Chapter Resources

Principles and Problems - Weebly · • Physicists often use the language of mathematics. • Physicists rely on theories and experiments with numerical results to support their conclusions.

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