The Branches of Physics Chapter 1 Section 1 What Is Physics? The Branches of Physics Click below to watch the Visual Concept. Visual Concept

The Branches of Physics Chapter 1 Section 1 What Is Physics? The Branches of Physics

Chapter 1 Section 1 What Is Physics? 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.

Physics and Technology Chapter 1 Section 1 What Is Physics? Physics and Technology

Chapter 1 The Scientific Method Section 1 What Is Physics? 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. Section 1 What Is Physics? 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. Section 1 What Is Physics? 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 Section 1 What Is Physics? 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).

Chapter 1 Preview Numbers as Measurements Dimensions and Units Section 2 Measurements in Experiments Chapter 1 Preview Numbers as Measurements Dimensions and Units Accuracy and Precision Significant Figures Vectors Distance/Displacement Speed\Velocity

Section 2 Measurements in Experiments Chapter 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 Section 2 Measurements in Experiments Chapter 1 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).

Section 2 Measurements in Experiments Chapter 1 SI Standards

Section 2 Measurements in Experiments Chapter 1 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 Section 2 Measurements in Experiments Chapter 1 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.

Accuracy and Precision Section 2 Measurements in Experiments Chapter 1 Accuracy and Precision Click below to watch the Visual Concept. Visual Concept

Measurement and Parallax Section 2 Measurements in Experiments Chapter 1 Measurement and Parallax Click below to watch the Visual Concept. Visual Concept

Chapter 1 Significant Figures Section 2 Measurements in Experiments Chapter 1 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 Section 2 Measurements in Experiments Chapter 1 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.

Rules for Determining Significant Zeroes Section 2 Measurements in Experiments Chapter 1 Rules for Determining Significant Zeroes Click below to watch the Visual Concept. Visual Concept

Rules for Determining Significant Zeros Section 2 Measurements in Experiments Chapter 1 Rules for Determining Significant Zeros

Rules for Calculating with Significant Figures Section 2 Measurements in Experiments Chapter 1 Rules for Calculating with Significant Figures

Rules for Rounding in Calculations Section 2 Measurements in Experiments Chapter 1 Rules for Rounding in Calculations Click below to watch the Visual Concept. Visual Concept

Rules for Rounding in Calculations Section 2 Measurements in Experiments Chapter 1 Rules for Rounding in Calculations

Chapter 1 Preview Objectives Mathematics and Physics Physics Equations Section 3 The Language of Physics Chapter 1 Preview Objectives Mathematics and Physics Physics Equations

Section 3 The Language of Physics Chapter 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.

Mathematics and Physics Section 3 The Language of Physics 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.

Data from Dropped-Ball Experiment 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.

Graph from Dropped-Ball Experiment Section 3 The Language of Physics 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 Section 3 The Language of Physics 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.

Equation from Dropped-Ball Experiment Section 3 The Language of Physics Chapter 1 Equation from Dropped-Ball Experiment 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 D (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 3 Preview Objectives Scalars and Vectors Section 1 Introduction to Vectors Preview Objectives Scalars and Vectors Graphical Addition of Vectors Triangle Method of Addition Properties of Vectors

Chapter 3 Scalars and Vectors Section 1 Introduction to Vectors 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.

Graphical Addition of Vectors Chapter 3 Section 1 Introduction to Vectors 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.

Triangle Method of Addition Chapter 3 Section 1 Introduction to Vectors 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.

Triangle Method of Addition Chapter 3 Section 1 Introduction to Vectors Triangle Method of Addition Click below to watch the Visual Concept. Visual Concept

Chapter 3 Properties of Vectors Section 1 Introduction to Vectors Click below to watch the Visual Concept. Visual Concept

Coordinate Systems in Two Dimensions Chapter 3 Section 2 Vector Operations 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.

Determining Resultant Magnitude and Direction Chapter 3 Section 2 Vector Operations 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.

Determining Resultant Magnitude and Direction, continued Chapter 3 Section 2 Vector Operations 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.

Determining Resultant Magnitude and Direction, continued Chapter 3 Section 2 Vector Operations 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.

Resolving Vectors into Components Chapter 3 Section 2 Vector Operations 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.

Resolving Vectors into Components, continued Chapter 3 Section 2 Vector Operations 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 the airplane’s vertical speed.

Resolving Vectors into Components, continued Chapter 3 Section 2 Vector Operations 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.

Adding Vectors That Are Not Perpendicular Chapter 3 Section 2 Vector Operations 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

Adding Vectors That Are Not Perpendicular, continued Chapter 3 Section 2 Vector Operations 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.

Chapter 3 Section 4 Relative Motion Objectives Describe situations in terms of frame of reference. Solve problems involving relative velocity.

Chapter 3 Frames of Reference Section 4 Relative Motion 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.

Frames of Reference, continued Chapter 3 Section 4 Relative Motion Frames of Reference, continued Consider 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.

Chapter 3 Relative Motion Section 4 Relative Motion Click below to watch the Visual Concept. Visual Concept

Chapter 3 Relative Velocity Section 4 Relative Motion 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

Chapter 2 Preview Objectives One Dimensional Motion Displacement Section 1 Displacement and Velocity Chapter 2 Preview Objectives One Dimensional Motion Displacement Average Velocity Velocity and Speed Interpreting Velocity Graphically

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.

One Dimensional Motion Section 1 Displacement and Velocity 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.

Chapter 2 Frame of Reference Section 1 Displacement and Velocity Click below to watch the Visual Concept. Visual Concept

displacement = final position – initial position Section 1 Displacement and Velocity Chapter 2 Displacement Displacement is a change in position. Displacement is not always equal to the distance traveled. The SI unit of displacement is the meter, m. x = xf – xi displacement = final position – initial position

Chapter 2 Displacement Section 1 Displacement and Velocity Click below to watch the Visual Concept. Visual Concept

Positive and Negative Displacements Section 1 Displacement and Velocity Chapter 2 Positive and Negative Displacements

Chapter 2 Average Velocity Section 1 Displacement and Velocity Chapter 2 Average Velocity Average velocity is the total displacement divided by the time interval during which the displacement occurred. In SI, the unit of velocity is meters per second, abbreviated as m/s.

Chapter 2 Average Velocity Section 1 Displacement and Velocity Click below to watch the Visual Concept. Visual Concept

Chapter 2 Velocity and Speed Section 1 Displacement and 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.

Interpreting Velocity Graphically Section 1 Displacement and Velocity Chapter 2 Interpreting Velocity Graphically 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. Object 1: positive slope = positive velocity Object 2: zero slope= zero velocity Object 3: negative slope = negative velocity

Interpreting Velocity Graphically, continued Section 1 Displacement and Velocity Chapter 2 Interpreting Velocity Graphically, continued The instantaneous velocity is the velocity of an object at some instant or at a specific point in the object’s path. 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.

Sign Conventions for Velocity Section 1 Displacement and Velocity Chapter 2 Sign Conventions for Velocity Click below to watch the Visual Concept. Visual Concept