© houghton mifflin harcourt publishing company click below to watch the visual concept. visual...

© Houghton Mifflin Harcourt Publishing Company

Click below to watch the Visual Concept.

Visual Concept

Chapter 1 Section 1 What Is Physics?

The Branches of Physics


Chapter 1

The Branches of Physics

Section 1 What Is Physics?


Chapter 1

Physics

• The goal of physics is to use a small number of basic concepts, equations, and assumptions to describe the physical world.

• These physics principles can then be used to make predictions about a broad range of phenomena.

• Physics discoveries often turn out to have unexpected practical applications, and advances in technology can in turn lead to new physics discoveries.



Chapter 1

Physics and Technology



Chapter 1

The Scientific Method

• There is no single procedure that scientists follow in their work. However, there are certain steps common to all good scientific investigations.

• These steps are called the scientific method.



Chapter 1

Models

• Physics uses models that describe phenomena.

• A model is a pattern, plan, representation, or description designed to show the structure or workings of an object, system, or concept.

• A set of particles or interacting components considered to be a distinct physical entity for the purpose of study is called a system.



Chapter 1

Hypotheses

• Models help scientists develop hypotheses.

• A hypothesis is an explanation that is based on prior scientific research or observations and that can be tested.

• The process of simplifying and modeling a situation can help you determine the relevant variables and identify a hypothesis for testing.



Chapter 1

Hypotheses, continued

Galileo modeled the behavior of falling objects in order to develop a hypothesis about how objects fall.

If heavier objects fell faster than slower ones,would two bricks of different masses tied together fall slower (b) or faster (c) than the heavy brick alone (a)? Because of this contradiction, Galileo hypothesized instead that all objects fall at the same rate, as in (d).



Section 2 Measurements in Experiments

Preview

• Numbers as Measurements

• Dimensions and Units

• Accuracy and Precision

• Significant Figures

• Vectors

• Distance/Displacement Speed\Velocity

Chapter 1


Section 2 Measurements in ExperimentsChapter 1

Objectives

• List basic SI units and the quantities they describe.

• Convert measurements into scientific notation.

• Distinguish between accuracy and precision.

• Use significant figures in measurements and calculations.



Numbers as Measurements

• In SI, the standard measurement system for science, there are seven base units.

• Each base unit describes a single dimension, such as length, mass, or time.

• The units of length, mass, and time are the meter (m), kilogram (kg), and second (s), respectively.

• Derived units are formed by combining the seven base units with multiplication or division. For example, speeds are typically expressed in units of meters per second (m/s).


Chapter 1

SI Standards




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.



Accuracy and Precision

• Accuracy is a description of how close a measurement is to the correct or accepted value of the quantity measured.

• Precision is the degree of exactness of a measurement.

• A numeric measure of confidence in a measurement or result is known as uncertainty. A lower uncertainty indicates greater confidence.



Visual Concept

Chapter 1Section 2 Measurements in Experiments

Accuracy and Precision



Visual Concept


Measurement and Parallax



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.



Significant Figures, continued

Even though this ruler is marked in only centimeters and half-centimeters, if you estimate, you can use it to report measurements to a precision of a millimeter.



Visual Concept


Rules for Determining Significant Zeroes


Chapter 1

Rules for Determining Significant Zeros



Chapter 1

Rules for Calculating with Significant Figures




Visual Concept


Rules for Rounding in Calculations


Chapter 1

Rules for Rounding in Calculations



Preview

• Objectives

• Mathematics and Physics

• Physics Equations

Chapter 1Section 3 The Language of Physics


Section 3 The Language of PhysicsChapter 1

Objectives

• Interpret data in tables and graphs, and recognize equations that summarize data.

• Distinguish between conventions for abbreviating units and quantities.

• Use dimensional analysis to check the validity of equations.

• Perform order-of-magnitude calculations.


Chapter 1

Mathematics and Physics

• Tables, graphs, and equations can make data easier to understand.

• For example, consider an experiment to test Galileo’s hypothesis that all objects fall at the same rate in the absence of air resistance.

– In this experiment, a table-tennis ball and a golf ball are dropped in a vacuum. – The results are recorded as a set of numbers corresponding to the times of the fall

and the distance each ball falls.– A convenient way to organize the data is to form a table, as shown on the next

slide.

Section 3 The Language of Physics


Chapter 1

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.


Chapter 1

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. a

The shape of the graph provides information about the relationship between time and distance.


Chapter 1

Physics Equations• Physicists use equations to describe measured or predicted relationships between physical

quantities.

• Variables and other specific quantities are abbreviated with letters that are boldfaced or italicized.

• Units are abbreviated with regular letters, sometimes called roman letters.

• Two tools for evaluating physics equations are dimensional analysis and order-of-magnitude estimates.



• We can use the following equation to describe the relationship between the variables in the dropped-ball experiment:

(change in position in meters) = 4.9 (time in seconds)2

• With symbols, the word equation above can be written as follows:

y = 4.9(t)2

• The Greek letter (delta) means “change in.” The abbreviation y indicates the vertical change in a ball’s position from its starting point, and t indicates the time elapsed.

• This equation allows you to reproduce the graph and make predictions about the change in position for any time.

Chapter 1

Equation from Dropped-Ball Experiment



Preview

• Objectives

• Scalars and Vectors

• Graphical Addition of Vectors

• Triangle Method of Addition

• Properties of Vectors

Chapter 3 Section 1 Introduction to Vectors


Chapter 3

Scalars and Vectors

• A scalar is a physical quantity that has magnitude but no direction.– Examples: speed, volume, the number of pages

in your textbook

• A vector is a physical quantity that has both magnitude and direction.– Examples: displacement, velocity, acceleration

• In this book, scalar quantities are in italics. Vectors are represented by boldface symbols.

Section 1 Introduction to Vectors


Chapter 3

Graphical Addition of Vectors

• A resultant vector represents the sum of two or more vectors.

• Vectors can be added graphically.

A student walks from his house to his friend’s house (a), then from his friend’s house to the school (b). The student’s resultant displacement (c) can be found by using a ruler and a protractor.



Chapter 3

Triangle Method of Addition

• Vectors can be moved parallel to themselves in a diagram.

• Thus, you can draw one vector with its tail starting at the tip of the other as long as the size and direction of each vector do not change.

• The resultant vector can then be drawn from the tail of the first vector to the tip of the last vector.




Visual Concept


Triangle Method of Addition



Visual Concept


Properties of Vectors


Chapter 3

Coordinate Systems in Two Dimensions

• One method for diagraming the motion of an object employs vectors and the use of the x- and y-axes.

• Axes are often designated using fixed directions.

• In the figure shown here, the positive y-axis points north and the positive x-axis points east.

Section 2 Vector Operations


Chapter 3

Determining Resultant Magnitude and Direction• In Section 1, the magnitude and direction of a

resultant were found graphically.

• With this approach, the accuracy of the answer depends on how carefully the diagram is drawn and measured.

• A simpler method uses the Pythagorean theorem and the tangent function.



Chapter 3

Determining Resultant Magnitude and Direction, continued

The Pythagorean Theorem

• Use the Pythagorean theorem to find the magnitude of the resultant vector.

• The Pythagorean theorem states that for any right triangle, the square of the hypotenuse—the side opposite the right angle—equals the sum of the squares of the other two sides, or legs.

c2 a2 b2

(hypotenuse)2 (leg 1)2 (leg 2)2



Chapter 3

Determining Resultant Magnitude and Direction, continued

The Tangent Function

• Use the tangent function to find the direction of the resultant vector.

• For any right triangle, the tangent of an angle is defined as the ratio of the opposite and adjacent legs with respect to a specified acute angle of a right triangle.

tangent of angle = opposite leg

adjacent leg



Chapter 3

Resolving Vectors into Components

• You can often describe an object’s motion more conveniently by breaking a single vector into two components, or resolving the vector.

• The components of a vector are the projections of the vector along the axes of a coordinate system.

• Resolving a vector allows you to analyze the motion in each direction.



Chapter 3

Resolving Vectors into Components, continued

Consider an airplane flying at 95 km/h.• The hypotenuse (vplane) is the resultant vector

that describes the airplane’s total velocity.

• The adjacent leg represents the x component (vx), which describes the airplane’s horizontal speed.

• The opposite leg represents

the y component (vy), which describes theairplane’s vertical speed.



Chapter 3

Resolving Vectors into Components, continued

• The sine and cosine functions can be used to find the components of a vector.

• The sine and cosine functions are defined in terms of the lengths of the sides of right triangles.

sine of angle =

opposite leg

hypotenuse

cosine of angle = adjacent leg

hypotenuse



Chapter 3

Adding Vectors That Are Not Perpendicular

• Suppose that a plane travels first 5 km at an angle

of 35°, then climbs at 10° for 22 km, as shown below. How can you find the total displacement?

• Because the original displacement vectors do not form a right triangle, you can not directly apply the tangent function or the Pythagorean theorem.

d2

d1



Chapter 3

Adding Vectors That Are Not Perpendicular, continued

• You can find the magnitude and the direction of the resultant

by resolving each of the plane’s displacement vectors into its x and y components.

• Then the components along each axis can be added together.

As shown in the figure, these sums will be the two perpendicular components of the resultant, d. The resultant’s magnitude can then be found by using the Pythagorean theorem, and its direction can be found by using the inverse tangent function.



Section 4 Relative MotionChapter 3

Objectives

• Describe situations in terms of frame of reference.

• Solve problems involving relative velocity.


Chapter 3

Frames of Reference• If you are moving at 80 km/h north and a car

passes you going 90 km/h, to you the faster car seems to be moving north at 10 km/h.

• Someone standing on the side of the road would measure the velocity of the faster car as 90 km/h toward the north.

• This simple example demonstrates that velocity measurements depend on the frame of reference of the observer.

Section 4 Relative Motion


Chapter 3

Frames of Reference, continuedConsider a stunt dummy dropped from a plane.(a) When viewed from the plane, the stunt dummy falls straight

down. (b) When viewed from a stationary position on the ground, the

stunt dummy follows a parabolic projectile path.




Visual Concept

Chapter 3 Section 4 Relative Motion

Relative Motion


Chapter 3

Relative Velocity• When solving relative velocity problems, write down the

information in the form of velocities with subscripts.

• Using our earlier example, we have:• vse = +80 km/h north (se = slower car with respect to

Earth)• vfe = +90 km/h north (fe = fast car with respect to Earth)• unknown = vfs (fs = fast car with respect to slower car)

• Write an equation for vfs in terms of the other velocities. The subscripts start with f and end with s. The other subscripts start with the letter that ended the preceding velocity: • vfs = vfe + ves



Preview

• Objectives

• One Dimensional Motion

• Displacement

• Average Velocity

• Velocity and Speed

• Interpreting Velocity Graphically

Chapter 2

Section 1 Displacement and Velocity



Chapter 2

Objectives

• Describe motion in terms of frame of reference, displacement, time, and velocity.

• Calculate the displacement of an object traveling at a known velocity for a specific time interval.

• Construct and interpret graphs of position versus time.



Chapter 2

One Dimensional Motion

• To simplify the concept of motion, we will first consider motion that takes place in one direction.

• One example is the motion of a commuter train on a straight track.

• To measure motion, you must choose a frame of reference. A frame of reference is a system for specifying the precise location of objects in space and time.



Visual Concept

Chapter 2


Frame of Reference



Chapter 2

Displacement

x = xf – xi displacement = final position – initial position

• Displacement is a change in position.

• Displacement is not always equal to the distance traveled.

• The SI unit of displacement is the meter, m.



Visual Concept

Chapter 2


Displacement


Chapter 2

Positive and Negative Displacements




Chapter 2

Average Velocity

• Average velocity is the total displacement divided by the time interval during which the displacement occurred.

f iavg

f i

x xxv

t t t

average velocity = change in position

change in time =

displacement

time interval

• In SI, the unit of velocity is meters per second, abbreviated as m/s.



Visual Concept

Chapter 2


Average Velocity



Chapter 2

Velocity and Speed

• Velocity describes motion with both a direction and a numerical value (a magnitude).

• Speed has no direction, only magnitude.

• Average speed is equal to the total distance traveled divided by the time interval.

distance traveledaverage speed =

time of travel



Chapter 2

Interpreting Velocity Graphically

– Object 1: positive slope = positive velocity

– Object 2: zero slope= zero velocity – Object 3: negative slope = negative

velocity

• For any position-time graph, we can determine the average velocity by drawing a

straight line between any two points on the graph.

• If the velocity is constant, the graph of position versus time is a

straight line. The slope indicates the velocity.



Chapter 2

Interpreting Velocity Graphically, continued

The instantaneous

velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph.

The instantaneous velocity is the velocity of an object at some instant or at a

specific point in the object’s path.



Visual Concept

Chapter 2


Sign Conventions for Velocity

© houghton mifflin harcourt publishing company click below to watch the visual concept. visual...

Documents

models physics

branches of physics

branches of physics

goal of physics

physics principles

experiments chapter

new physics discoveries

technology section