ap physics, unit 1, days 1-2 objects in motion. welcome, please find your seat, take out your summer...

AP PHYSICS, UNIT 1, DAYS 1-2

Objects in Motion

WELCOME, PLEASE FIND YOUR SEAT, TAKE OUT YOUR SUMMER HOMEWORK AND A COMPOSITION NOTEBOOK.

SUMMER HOMEWORK CHECK

CLASSROOM EXPECTATIONS

1) Respect the lab equipment. All lab equipment.

2) Respect each other.

3) Try. And don’t be afraid to ask questions.

4) Work with a sense of urgency.

5) Don’t leave trash in the desk.

ABOUT THE AP PHYSICS TEST VERY heavy emphasis on the conceptual

But the mathematical is still necessary

VERY heavy emphasis on lab work and exploration

ABOUT THE AP PHYSICS CLASS Your lab notebook will be for labs only. All lab information will be recorded in there. All formal lab reports (and many informal ones) will be written in there. Write neatly. Do NOT erase.

Homework will contain both readings and practice.

LAB NOTEBOOK HEADER

OBJECTS IN MOTION LAB

WELCOME BACK!

Homework Check

CONSTANT VELOCITY LECTURE You do NOT need to take notes on everything. Rather, add to your reading notes, or highlight information that seems especially important.

For the first couple of lectures, I will be a lot more specific with what you should and should not write down, as you get used to learning from lecture in science.

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Chapter 1 Representing Motion

Chapter Goal: To introduce the fundamental concepts of motion and to review related basic mathematical principles.

© 2015 Pearson Education, Inc.

12

Chapter 1 PreviewLooking Ahead: Describing Motion

• This series of images of a skier clearly shows his motion. Such visual depictions are a good first step in describing motion.

• You’ll learn to make motion diagrams that provide a simplified view of the motion of an object.


Section 1.1 Motion: A First Look


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Types of Motion

• Motion is the change of an object’s position or orientation with time.

• The path along which an object moves is called the object’s trajectory.


15

Making a Motion Diagram

• These motion diagrams in one dimension show objects moving at constant speed (skateboarder), speeding up (runner) and slowing down (car).


16

Making a Motion Diagram

• This motion diagram shows motion in two dimensions with changes in both speed and direction.


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Motion diagrams are made of two cars. Both have the same time interval between photos. Which car, A or B, is going slower?

Car A Car B

QuickCheck 1.1


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Motion diagrams are made of two cars. Both have the same time interval between photos. Which car, A or B, is going slower?

Car A Car B

QuickCheck 1.1


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The Particle Model

• The particle model of motion is a simplification in which we treat a moving object as if all of its mass were concentrated at a single point


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QuickCheck 1.2

Two runners jog along a track. The positions are shown at 1 s intervals. Which runner is moving faster?


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QuickCheck 1.2

Two runners jog along a track. The positions are shown at 1 s intervals. Which runner is moving faster?


A

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QuickCheck 1.3

Two runners jog along a track. The times at each position are shown. Which runner is moving faster?

A. Runner AB. Runner BC. Both runners are moving at the same speed.


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QuickCheck 1.3

Two runners jog along a track. The times at each position are shown. Which runner is moving faster?

A. Runner AB. Runner BC. Both runners are moving at the same speed.


Section 1.2 Position and Time:Putting Numbers on Nature


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Position and Coordinate Systems

• To specify position we need a reference point (the origin), a distance from the origin, and a direction from the origin.

• The combination of an origin and an axis marked in both the positive and negative directions makes a coordinate system.


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Position and Coordinate Systems

• The symbol that represents a position along an axis is called a coordinate.


27

Time

• For a complete motion diagram we need to label each frame with its corresponding time (symbol t) as read off a clock.


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Changes in Position and Displacement

• A change of position is called a displacement.

• Displacement is the difference between a final position and an initial position:


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Change in Time

• In order to quantify motion, we’ll need to consider changes in time, which we call time intervals.

• A time interval Δt measures the elapsed time as an object moves from an initial position xi at time ti to a final position xf at time tf. Δt is always positive.


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Example 1.1 How long a ride?

Carol is enjoying a bicycle ride on a country road that runs east-west past a water tower. Define a coordinate system so that increasing x means moving east. At noon, Carol is 3 miles (mi) east of the water tower. A half-hour later, she is 2 mi west of the water tower. What is her displacement during that half-hour?

PREPARE Although it may seem like overkill for such a simple problem, you should start by making a drawing, like the one in FIGURE 1.15, with the x-axis along the road.


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Example 1.1 How long a ride? (cont.)

SOLVE We’ve specified values for Carol’s initial and final positions in our drawing. We can thus compute her displacement:

Δx = xf xi = ( 2 mi) (3 mi) = 5 mi

ASSESS Carol is moving to the west, so we expect her displacement to be negative—and it is. We can see from our drawing in Figure 1.15 that she has moved 5 miles from her starting position, so our answer seems reasonable. Carol travels 5 miles in a half-hour, quite a reasonable pace for a cyclist.


32

QuickCheck 1.4

Maria is at position x = 23 m. She then undergoes a displacement x = –50 m. What is her final position?

A. –27 mB. –50 mC. 23 mD. 73 m


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QuickCheck 1.4

Maria is at position x = 23 m. She then undergoes a displacement x = –50 m. What is her final position?

A. –27 mB. –50 mC. 23 mD. 73 m


34

QuickCheck 1.5

An ant zig-zags back and forth on a picnic table as shown.

The ant’s distance traveled and displacement are

A. 50 cm and 50 cmB. 30 cm and 50 cmC. 50 cm and 30 cmD. 50 cm and –50 cmE. 50 cm and –30 cm


35

QuickCheck 1.5

An ant zig-zags back and forth on a picnic table as shown.

The ant’s distance traveled and displacement are

A. 50 cm and 50 cmB. 30 cm and 50 cmC. 50 cm and 30 cmD. 50 cm and –50 cmE. 50 cm and –30 cm


Section 1.3 Velocity


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Velocity and Speed

• Motion at a constant speed in a straight line is called uniform motion.


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Example Problem

Jane walks to the right at a constant rate, moving 3 m in 3 s. At t = 0 s she passes the x = 1 m mark. Draw her motion diagram from t = –1 s to t = 4 s.


39

Velocity and Speed

• Speed measures only how fast an object moves, but velocity tells us both an object’s speed and its direction.

• The velocity defined by Equation 1.2 is called the average velocity.


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Example 1.2 Finding the speed of a seabird

Albatrosses are seabirds that spend most of their lives flying over the ocean looking for food. With a stiff tailwind, an albatross can fly at high speeds. Satellite data on one particularly speedy albatross showed it 60 miles east of its roost at 3:00 PM and then, at 3:15 PM, 80 miles east of its roost. What was its velocity?


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Example 1.2 Finding the speed of a seabird (cont.)

PREPARE The statement of the problem provides us with a natural coordinate system: We can measure distances with respect to the roost, with distances to the east as positive. With this coordinate system, the motion of the albatross appears as in FIGURE 1.18. The motion takes place between 3:00 and 3:15, a time interval of 15 minutes, or 0.25 hour.

SOLVE We know the initial and final positions, and we know the time interval, so we can calculate the velocity:


42

Example Problem

At t = 12 s, Frank is at x = 25 m. 5 s later, he’s at x = 20 m. What is Frank’s velocity?

This example indicates that velocities to the left are negative. The information that t = 12 s is extraneous.


43

Example Problem

Jenny runs 1 mi to the northeast, then 1 mi south. Graphically find her net displacement.


44

Chapter 2 Motion in One Dimension

Chapter Goal: To describe and analyze linear motion.


45

Chapter 2 PreviewLooking Ahead: Uniform Motion

• Successive images of the rider are the same distance apart, so the velocity is constant. This is uniform motion.

• You’ll learn to describe motion in terms of quantities such as distance and velocity, an important first step in analyzing motion.


Section 2.1 Describing Motion


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Representing Position

• We will use an x-axis to analyze horizontal motion and motion on a ramp, with the positive end to the right.

• We will use a y-axis to analyze vertical motion, with the positive end up.


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Representing Position

The motion diagram of a student walking to school and acoordinate axis for making measurements

• Every dot in the motion diagram of Figure 2.2 represents the student’s position at a particular time.

• Figure 2.3 shows the student’s motion shows the student’s position as a graph of x versus t.


49

From Position to Velocity

• On a position-versus-time graph, a faster speed corresponds to a steeper slope.

• The slope of an object’s position-versus-time graph is the object’s velocity at that point in the motion.


50

From Position to Velocity

• We can deduce the velocity-versus-time graph from the position-versus-time graph.

• The velocity-versus-time graph is yet another way to represent an object’s motion.


51

QuickCheck 2.2

Here is a motion diagram of a car moving along a straight road:

Which velocity-versus-time graph matches this motion diagram?

E. None of the above.© 2015 Pearson Education, Inc.

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QuickCheck 2.2



E. None of the above.© 2015 Pearson Education, Inc.

C.

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QuickCheck 2.3




54

QuickCheck 2.3




D.

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A graph of position versus time for a basketball player moving down the court appears as follows:

Which of the following velocity graphs matches the position graph?

QuickCheck 2.4


C. D.B.A.

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A graph of position versus time for a basketball player moving down the court appears as follows:

Which of the following velocity graphs matches the position graph?

QuickCheck 2.4


C. D.B.A.

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Example 2.2 Analyzing a car’s position graph

FIGURE 2.11 gives the position-versus-time graph of a car.

a. Draw the car’s velocity-versus-time graph.

b. Describe the car’s motion in words.

PREPARE Figure 2.11 is a graphical representation of the motion. The car’s position-versus-time graph is a sequence of three straight lines. Each of these straight lines represents uniform motion at a constant velocity. We can determine the car’s velocity during each interval of time by measuring the slope of the line.


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Example 2.2 Analyzing a car’s position graph (cont.)

SOLVE

a. From t = 0 s to t = 2 s (Δt = 2 s) the car’s displacement is Δx = 4 m 0 m = 4 m. The velocity during this interval is

The car’s position does not change from t = 2 s to t = 4 s (Δx = 0 m), so vx = 0 m/s. Finally, the displacement between t = 4 s and t = 6 s (Δt = 2 s) is Δx = 10 m. Thus the velocity during this interval is

These velocities are represented graphically in FIGURE 2.12.© 2015 Pearson Education, Inc.

59

Example 2.2 Analyzing a car’s position graph (cont.)

SOLVE

b. The velocity-versus-time graph of Figure 2.12 shows the motion in a way that we can describe in a straightforward manner: The car backs up for 2 s at 2 m/s, sits at rest for 2 s, then drives forward at 5 m/s for 2 s.

ASSESS Notice that the velocity graph and the position graph look completely different. They should! The value of the velocity graph at any instant of time equals the slope of the position graph. Since the position graph is made up of segments of constant slope, the velocity graph should be made up of segments of constant value, as it is. This gives us confidence that the graph we have drawn is correct.


60

From Velocity to Position

• We can deduce the position-versus-time graph from the velocity-versus-time graph.

• The sign of the velocity tells us whether the slope of the position graph is positive or negative.

• The magnitude of the velocity tells us how steep the slope is.


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QuickCheck 2.1


Which position-versus-time graph matches this motion diagram?


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QuickCheck 2.1


Which position-versus-time graph matches this motion diagram?


E.

63

QuickCheck 2.6

A graph of velocity versus time for a hockey puck shot into a goal appears as follows:

Which of the following position graphs matches the velocity graph?


C. D.B.A.

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QuickCheck 2.6

A graph of velocity versus time for a hockey puck shot into a goal appears as follows:

Which of the following position graphs matches the velocity graph?


(d)C. D.B.A.

Section 2.2 Uniform Motion


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Uniform Motion

• Straight-line motion in which equal displacements occur during any successive equal-time intervals is called uniform motion or constant-velocity motion.

• An object’s motion is uniform if and only if its position-versus-time graph is a straight line.


67

Equations of Uniform Motion

• The velocity of an object in uniform motion tells us the amount by which its position changes during each second.

• The displacement Δx is proportional to the time interval Δt.


69

QuickCheck 2.8

Here is a position graph of an object:

At t = 1.5 s, the object’s velocity is

A. 40 m/sB. 20 m/sC. 10 m/sD. –10 m/sE. None of the above


70

QuickCheck 2.8

Here is a position graph of an object:

At t = 1.5 s, the object’s velocity is

A. 40 m/sB. 20 m/sC. 10 m/sD. –10 m/sE. None of the above


71

Example 2.3 If a train leaves Cleveland at 2:00…

A train is moving due west at a constant speed. A passenger notes that it takes 10 minutes to travel 12 km. How long will it take the train to travel 60 km?

PREPARE For an object in uniform motion, Equation 2.5 shows that the distance traveled Δx is proportional to the time interval Δt, so this is a good problem to solve using ratio reasoning.


72

Example 2.3 If a train leaves Cleveland at 2:00…(cont.)

SOLVE We are comparing two cases: the time to travel 12 km and the time to travel 60 km. Because Δx is proportional to Δt, the ratio of the times will be equal to the ratio of the distances. The ratio of the distances is

This is equal to the ratio of the times:

It takes 10 minutes to travel 12 km, so it will take 50 minutes—5 times as long—to travel 60 km.


73

Example Problem

A soccer player is 15 m from her opponent’s goal. She kicks the ball hard; after 0.50 s, it flies past a defender who stands 5 m away, and continues toward the goal. How much time does the goalie have to move into position to block the kick from the moment the ball leaves the kicker’s foot?


74

From Velocity to Position, One More Time

• The displacement Δx is equal to the area under the velocity graph during the time interval Δt.


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QuickCheck 2.11

Here is the velocity graph of an object that is at the origin (x 0 m) at t 0 s.

At t 4.0 s, the object’s position is

A. 20 mB. 16 mC. 12 mD. 8 mE. 4 m


76

QuickCheck 2.11

Here is the velocity graph of an object that is at the origin (x 0 m) at t 0 s.

At t 4.0 s, the object’s position is

A. 20 mB. 16 mC. 12 mD. 8 mE. 4 m


Displacement area under the curve

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ap physics, unit 1, days 1-2 objects in motion. welcome, please find your seat, take out your summer...

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