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Chapter Goal: To introduce the fundamental concepts of motion.

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Title: Chapter Goal: To introduce the fundamental concepts of motion.


1
Chapter 1 Concepts of Motion
Pickup PSE3e Photo from page 2, snowboarder jump.
  • Chapter Goal To introduce the fundamental
    concepts of motion.

Slide 1-2
2
Chapter 1 Preview
Slide 1-3
3
Chapter 1 Preview
Slide 1-4
4
  • Four basic types of motion

Slide 1-19
5
Making a Motion Diagram
  • Consider a movie of a moving object.
  • A movie camera takes photographs at a fixed rate
    (i.e., 30 photographs every second).
  • Each separate photo is called a frame.
  • The car is in a different position in each frame.
  • Shown are four frames in a filmstrip.

Slide 1-20
6
Making a Motion Diagram
  • Cut individual frames of the filmstrip apart.
  • Stack them on top of each other.
  • This composite photo shows an objects position
    at several equally spaced instants of time.
  • This is called a motion diagram.

Slide 1-21
7
Examples of Motion Diagrams
  • An object that has a single position in a motion
    diagram is at rest.
  • Example A stationary ball on the ground.
  • An object with images that are equally spaced is
    moving with constant speed.
  • Example A skateboarder rolling down the sidewalk.

Slide 1-22
8
Examples of Motion Diagrams
  • An object with images that have increasing
    distance between them is speeding up.
  • Example A sprinter starting the 100 meter dash.
  • An object with images that have decreasing
    distance between them is slowing down.
  • Example A car stopping for a red light.

Slide 1-23
9
Examples of Motion Diagrams
  • A motion diagram can show more complex motion in
    two dimensions.
  • Example A jump shot from center court.
  • In this case the ball is slowing down as it
    rises, and speeding up as it falls.

Slide 1-24
10
Position and Time
  • In a motion diagram it is useful to add numbers
    to specify where the object is and when the
    object was at that position.
  • Shown is the motion diagram of a basketball,
    with 0.5 s intervals between frames.
  • A coordinate system has been added to show (x,
    y).
  • The frame at t ? 0 is frame 0, when the ball is
    at the origin.
  • The balls position in frame 4 can be specified
    with coordinates (x4, y4) ? (12 m, 9 m) at time
    t4 ? 2.0 s.

Slide 1-31
11
Position as a Vector
  • Another way to locate the ball is to draw an
    arrow from the origin to the point representing
    the ball.
  • You can then specify the length and direction of
    the arrow.
  • This arrow is called the position vector of
    the object.
  • The position vector is an alternative form of
    specifying position.
  • It does not tell us anything different than the
    coordinates (x, y).

Slide 1-32
12
Tactics Vector Addition
Slide 1-33
13
Vector Addition Example Displacement
Sam is standing 50 ft east of the corner of 12th
Street and Vine. He then walks northeast for 100
ft to a second point. What is Sams change of
position?
  • Sams initial position is the vector .
  • Vector is his position after he finishes
    walking.
  • Sam has changed position, and a change in
    position is called a displacement.
  • His displacement is the vector labeled .

Slide 1-34
14
Definition of Displacement
  • The displacement of an object as it moves
    from an initial position to a final position
    is
  • The definition of involves vector
    subtraction.
  • With numbers, subtraction is the same as the
    addition of a negative number.
  • Similarly, with vectors

Slide 1-35
15
Tactics Vector Subtraction
Slide 1-36
16
Time Interval
  • Its useful to consider a change in time.
  • An object may move from an initial position
    at time ti to a final position at time tf.

A stopwatch is used to measure a time interval.
  • Different observers may choose different
    coordinate systems and different clocks, however,
    all observers find the same values for the
    displacement ? and the time interval ?t.

Slide 1-41
17
Average Speed, Average Velocity
  • To quantify an objects fastness or slowness, we
    define a ratio
  • Average speed does not include information about
    direction of motion.
  • The average velocity of an object during a time
    interval ?t, in which the object undergoes a
    displacement ? , is the vector

The victory goes to the runner with the highest
average speed.
Slide 1-42
18
Motion Diagrams with Velocity Vectors
  • The velocity vector is in the same direction as
    the displacement ? .
  • The length of is directly proportional to the
    length of ? .
  • Consequently, we may label the vectors connecting
    the dots on a motion diagram as velocity vectors
    .
  • Below is a motion diagram for a tortoise racing a
    hare.
  • The arrows are average velocity vectors.
  • The length of each arrow represents the average
    speed.

Slide 1-43
19
EXAMPLE 1.2 Accelerating Up a Hill
Motion diagram of a car accelerating up a hill.
Slide 1-44
20
Acceleration
  • Sometimes an objects velocity is constant as it
    moves.
  • More often, an objects velocity changes as it
    moves.
  • Acceleration describes a change in velocity.
  • Consider an object whose velocity changes from
    to during the time interval ?t.
  • The quantity is the change
    in velocity.
  • The rate of change of velocity is called the
    average acceleration

The Audi TT accelerates from 0 to 60 mph in 6 s.
Slide 1-45
21
Tactics Finding the Acceleration Vector
Slide 1-46
22
Tactics Finding the Acceleration Vector
  • Notice that the acceleration vectors goes beside
    the dots, not beside the velocity vectors.
  • That is because each acceleration vector is the
    difference between two velocity vectors on either
    side of a dot.

Slide 1-47
23
Speeding Up or Slowing Down?
  • When an object is speeding up, the acceleration
    and velocity vectors point in the same direction.
  • When an object is slowing down, the acceleration
    and velocity vectors point in opposite
    directions.
  • An objects velocity is constant if and only if
    its acceleration is zero.
  • In the motion diagrams to the right, one object
    is speeding up and the other is slowing down,
    but they both have acceleration vectors toward
    the right.

Slide 1-53
24
Tactics Determining the Sign of the Position,
Velocity, and Acceleration
Slide 1-56
25
Tactics Determining the Sign of the Position,
Velocity, and Acceleration
Slide 1-57
26
Tactics Determining the Sign of the Position,
Velocity, and Acceleration
Slide 1-58
27
Position-versus-Time Graphs
  • Below is a motion diagram, made at 1 frame per
    minute, of a student walking to school.
  • A motion diagram is one way to represent the
    students motion.
  • Another way is to make a graph of x versus t for
    the student

Slide 1-65
28
Example 1.7 Interpreting a Position Graph
Slide 1-66
29
Example 1.7 Interpreting a Position Graph
Slide 1-67
30
Example 1.9 Launching a Weather Rocket
Slide 1-74
31
Example 1.9 Launching a Weather Rocket
Slide 1-75
32
Example 1.9 Launching a Weather Rocket
Slide 1-76
33
Example 1.9 Launching a Weather Rocket
Slide 1-77
34
Units
  • Science is based on experimental measurements,
    and measurements require units.
  • The system of units in science is called le
    Système Internationale dunités or SI units.
  • The SI unit of time is the second, abbreviated
    s.
  • 1 s is defined as the time required for
    9,192,631,770 oscillations of the radio wave
    absorbed by a cesium-133 atom.
  • The SI unit of length is the meter, abbreviated
    m.
  • 1 m is defined as the distance traveled by light
    in a vacuum during 1/299,292,458 of a second.

An atomic clock at the National Institute of
Standards and Technology is the primary standard
of time.
Slide 1-78
35
Units
  • The SI unit of mass is the kilogram, abbreviated
    kg.
  • 1 kg is defined as the mass of the international
    standard kilogram, a polished platinum-iridium
    cylinder stored in Paris.
  • Many lengths, times, and masses are either much
    less or much greater than the standards of 1 m, 1
    s, and 1 kg.
  • We use prefixes to denote various powers of 10,
    which make it easier to talk about quantities.

Slide 1-79
36
Unit Conversions
  • It is important to be able to convert back and
    forth between SI units and other units.
  • One effective method is to write the conversion
    factor as a ratio equal to one.
  • Because multiplying by 1 does not change a
    value, these ratios are easily used for unit
    conversions.
  • For example, to convert the length 2.00 feet to
    meters, use the ratio
  • So that

Slide 1-80
37
Assessment
  • When problem solving, it is important to decide
    whether or not your final answer makes sense.
  • For example, if you are working a problem about
    automobile speeds and reach an answer of 35
    m/s, is this a realistic speed?
  • The table shows some approximate conversion
    factors that can be used to assess answers.
  • Using 1 m/s 2 mph, you find that 35 m/s is
    roughly 20 mph, a reasonable speed for a car.
  • If you reached an answer of 350 m/s, this would
    correspond to an unreasonable 700 mph, indicating
    that perhaps you made a calculation error.

Slide 1-81
38
Significant Figures
  • Its important in science and engineering to
    state clearly what you know about a situationno
    less, and no more.
  • For example, if you report a length as 6.2 m, you
    imply that the actual value is between 6.15 m and
    6.25 m and has been rounded to 6.2.
  • The number 6.2 has two significant figures.
  • More precise measurement could give more
    significant figures.
  • The appropriate number of significant figures is
    determined by the data provided.
  • Calculations follow the weakest link rule The
    input value with the smallest number of
    significant figures determines the number of
    significant figures to use in reporting the
    output value.

Slide 1-82
39
Determining significant figures.
Slide 1-83
40
Tactics Using Significant Figures
Slide 1-84
41
EXAMPLE 1.10 Using significant figures
Slide 1-85
42
Orders of Magnitude and Estimating
Some approximate lengths and masses Distance you
can drive in 1 hour 105 m Distance
across a college campus 1000 m Length of
your arm 1 m Length of your little
fingernail 0.01 m Thickness of a sheet of paper
104 m Small car 1000 kg Large human 100
kg Science textbook 1 kg Apple 0.1
kg Raisin 103 kg
  • In many cases a very rough estimate of a number
    is sufficient.
  • A one-significant-figure estimate or calculation
    is called an order-of-magnitude estimate.
  • An order-of-magnitude estimate is indicated by
    the symbol , which indicates even less precision
    than .

Slide 1-86
43
Chapter 1 Summary Slides
Slide 1-89
44
General Strategy
Slide 1-90
45
General Strategy
Slide 1-91
46
Important Concepts
Slide 1-92
47
Important Concepts
Slide 1-93
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