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PPT – Chapter Goal: To introduce the fundamental concepts of motion. PowerPoint presentation | free to download - id: 67d8ce-YzM3O

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Chapter 1 Concepts of Motion

Pickup PSE3e Photo from page 2, snowboarder jump.

- Chapter Goal To introduce the fundamental

concepts of motion.

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Chapter 1 Preview

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Chapter 1 Preview

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- Four basic types of motion

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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.

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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.

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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.

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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.

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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.

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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.

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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).

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Tactics Vector Addition

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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 .

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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

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Tactics Vector Subtraction

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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.

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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.

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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.

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EXAMPLE 1.2 Accelerating Up a Hill

Motion diagram of a car accelerating up a hill.

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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.

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Tactics Finding the Acceleration Vector

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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.

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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.

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Tactics Determining the Sign of the Position,

Velocity, and Acceleration

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Tactics Determining the Sign of the Position,

Velocity, and Acceleration

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Tactics Determining the Sign of the Position,

Velocity, and Acceleration

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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

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Example 1.7 Interpreting a Position Graph

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Example 1.7 Interpreting a Position Graph

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Example 1.9 Launching a Weather Rocket

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Example 1.9 Launching a Weather Rocket

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Example 1.9 Launching a Weather Rocket

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Example 1.9 Launching a Weather Rocket

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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.

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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.

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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

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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.

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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.

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Determining significant figures.

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Tactics Using Significant Figures

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EXAMPLE 1.10 Using significant figures

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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 .

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Chapter 1 Summary Slides

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General Strategy

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General Strategy

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Important Concepts

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Important Concepts

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