lecture 1 - physics

7/21/2019 Lecture 1 - Physics

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FOR SCIENTISTS AND ENGINEERSphysics

a strategic approachTHIRD EDITION

randall d. knight

2013 Pearson Education, Inc.

Chapter 1 Lecture


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Chapter Goal:To introduce the fundamentalconcepts of motion.

Chapter 1 Concepts ofMotion

Slide 1-2

Pickup PSE3e

Photo from page 2, snowboarder jump.


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Four basic types of motionSlide 1-19


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!

Consider a movie of amoving object.

! A movie camera takesphotographs at a fixed

rate (i.e., 30 photographsevery second).

! Each separate photo iscalled a frame.

!

The car is in a differentposition in each frame.

! Shown are four frames ina filmstrip.

Making a Motion Diagram

Slide 1-20


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!

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.

Making a Motion Diagram

Slide 1-21


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!

An object that has a single position in a motiondiagram 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.

Examples of Motion Diagrams

Slide 1-22


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!

An object with images that have increasing distancebetween 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



! 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



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

QuickCheck 1.1

Slide 1-25

Car A Car B



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

QuickCheck 1.1

Slide 1-26

Car A Car B


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! Often motion of the object as a whole is not influenced by

details of the objects size and shape.

! We only need to keep track of a single point on the

object.

!

So we can treat the object as if all its mass wereconcentrated into a single point.

! A mass at a single point in space is called a particle.

! Particles have no size, no shape and no top, bottom,

front or back.! Below is a motion diagram of a car stopping, using the

particle model.

The Particle Model

Slide 1-27


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Motion diagram of a rocket launch

The Particle Model

Slide 1-26

Motion Diagram in which the object is

represented as a particle


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Three motion diagrams are shown. Which is a dustparticle settling to the floor at constant speed, whichis a ball dropped from the roof of a building, andwhich is a descending rocket slowing to make a softlanding on Mars?

A.

(a) is dust, (b) is ball, (c) is rocket.

B.

(a) is ball, (b) is dust, (c) is rocket.

C.

(a) is rocket, (b) is dust, (c) is ball.D.

(a) is rocket, (b) is ball, (c) is dust.

E.

(a) is ball, (b) is rocket, (c) is dust.

QuickCheck 1.2

Slide 1-29


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Three motion diagrams are shown. Which is a dustparticle settling to the floor at constant speed, whichis a ball dropped from the roof of a building, andwhich is a descending rocket slowing to make a softlanding on Mars?

A.

(a) is dust, (b) is ball, (c) is rocket.

B. (a) is ball, (b) is dust, (c) is rocket.

C.

(a) is rocket, (b) is dust, (c) is ball.D.

(a) is rocket, (b) is ball, (c) is dust.

E.

(a) is ball, (b) is rocket, (c) is dust.

QuickCheck 1.2

Slide 1-30


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! In a motion diagram it is usefulto 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 intervalsbetween 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 withcoordinates (x4, y4) =(12 m, 9 m) at time t4=2.0 s.

Position and Time

Slide 1-31


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! 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).

Position as a Vector

Slide 1-32


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Tactics: Vector Addition

Slide 1-33


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! Sams initial position is thevector .

! Vector is his position after

he finishes walking.

! Sam has changed position,

and a change in position iscalled a displacement.

! His displacement is thevector labeled .

Vector Addition Example: Displacement

Slide 1-34

Sam is standing 50 ft east of the corner of 12thStreet and

Vine. He then walks northeast for 100 ft to a secondpoint. What is Sams change of position?


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!

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

Definition of Displacement

Slide 1-35

The negative of a vector.


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Tactics: Vector Subtraction

Slide 1-36

Q i kCh k 1 3


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Given vectors and , what is ?

QuickCheck 1.3

Slide 1-37

Q i kCh k 1 3


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QuickCheck 1.3

Slide 1-38

Q i kCh k 1 4


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QuickCheck 1.4

Slide 1-39

Q i kCh k 1 4


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QuickCheck 1.4

Slide 1-40

Ti I t l


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!

Different observers may choose different coordinatesystems and different clocks, however, allobservers find the same values for thedisplacement ! and the time interval !t.

Time Interval

Slide 1-41

A stopwatch is used to measure a timeinterval.

!

Its useful to consider achange in time.

!

An object may move from an

initial position at timetito a

final position at time tf.


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M ti Di ith V l it V t


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! 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.

Motion Diagrams with Velocity Vectors

Slide 1-43

EXAMPLE 1 2 A l ti U Hill


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EXAMPLE 1.2 Accelerating Up a Hill

Slide 1-44

Motion diagram of a car accelerating up a hill.

A l ti


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! 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:

Acceleration

Slide 1-45

The Audi TT accelerates from 0 to 60

mph in 6 s.

Tactics Finding the Acceleration Vector


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Tactics: Finding the Acceleration Vector

Slide 1-46



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! 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

QuickCheck 1 5


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A particle has velocity as it accelerates from 1 to 2.

What is its velocity vector as it moves away from

point 2 on its way to point 3?

QuickCheck 1.5

Slide 1-48

QuickCheck 1 5


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A particle has velocity as it accelerates from 1 to 2.

What is its velocity vector as it moves away from

point 2 on its way to point 3?

QuickCheck 1.5

Slide 1-49

The Complete Motion Diagram


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The Complete Motion Diagram

Slide 1-50

Example 1 5 Skiing Through the Woods


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Example 1.5 Skiing Through the Woods

Slide 1-51

Example 1 5 Skiing Through the Woods


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Example 1.5 Skiing Through the Woods

Slide 1-52

Speeding Up or Slowing Down?


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! 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 diagramsto the right, one objectis speeding up and the

other is slowing down,but they both haveacceleration vectorstoward the right.

Speeding Up or Slowing Down?

Slide 1-53

QuickCheck 1 6


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A cyclist riding at 20 mph sees a stop sign and actually comes to a

complete stop in 4 s. He then, in 6 s, returns to a speed of 15 mph.Which is his motion diagram?

QuickCheck 1.6

Slide 1-54

QuickCheck 1 6


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A cyclist riding at 20 mph sees a stop sign and actually comes to a

complete stop in 4 s. He then, in 6 s, returns to a speed of 15 mph.Which is his motion diagram?

QuickCheck 1.6

Slide 1-55

Tactics: Determining the Sign of the Position


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Tactics: Determining the Sign of the Position,Velocity, and Acceleration

Slide 1-56



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Slide 1-57



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Slide 1-58

QuickCheck 1 7


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A ball is tossed straight up in the air. At its very

highest point, the balls acceleration vector

A. Points up.

B.

Is zero.

C. Points down.

QuickCheck 1.7

Slide 1-59

QuickCheck 1 7


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A ball is tossed straight up in

the air. At its very highest

point, the balls acceleration

vector

A. Points up.

B. Is zero.

C. Points down.

QuickCheck 1.7

Slide 1-60

In fact, the acceleration vector

points down as the ball rises, at the

highest point, and as it falls.

QuickCheck 1 8


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The motion diagram shows a particle that is slowing

down. The sign of the position xand the sign of thevelocity vxare:

A. Position is positive, velocity is positive.

B. Position is positive, velocity is negative.

C.

Position is negative, velocity is positive.

D. Position is negative, velocity is negative.

QuickCheck 1.8

Slide 1-61

QuickCheck 1 8


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down. The sign of the position xand the sign of thevelocity vxare:

A. Position is positive, velocity is positive.

B. Position is positive, velocity is negative.

C.

Position is negative, velocity is positive.

D. Position is negative, velocity is negative.

QuickCheck 1.8

Slide 1-62

QuickCheck 1 9


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down. The sign of the acceleration axis:

A.

Acceleration is positive.

B.

Acceleration is negative.

QuickCheck 1.9

Slide 1-63

QuickCheck 1 9


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down. The sign of the acceleration axis:

A. Acceleration is positive.

B.

Acceleration is negative.

QuickCheck 1.9

Slide 1-64

Position-versus-Time Graphs


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! 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 xversus tfor thestudent:

Position versus Time Graphs

Slide 1-65

Example 1.7 Interpreting a Position Graph


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Slide 1-66



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Slide 1-67

QuickCheck 1.10


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This is a graph of an object

moving along a straight line.The most likely interpretation is:

A.

A person walking down a

steep mountain.

B.

A car that drives and stops

and drives and stops.

C.

An elevator descending.

D.

A rock that falls, bounces,and falls some more.

E.

A ball that is hit, caught,

and thrown to someone else.

QuickCheck 1.10

Slide 1-68

QuickCheck 1.10


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This is a graph of an object

moving along a straight line.The most likely interpretation is:

A.

A person walking down a

steep mountain.

B.

A car that drives and stops

and drives and stops.

C. An elevator descending.

D.

A rock that falls, bounces,and falls some more.

E.

A ball that is hit, caught,

and thrown to someone else.

QuickCheck 1.10

Slide 1-69

Vertical motion

About 150 feet in 50 s

Solving Problems in Physics


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A new building requires careful planning. Thearchitects visualization and drawings have to becomplete before the detailed procedures of

construction get under way. The same is true forsolving problems in physics.

! Physics problems are often presented

using words, which can be imprecise

or ambiguous.

! Part of problem-solving involves

using symbols and drawings tocreate a representation, which

is clear and precise.

! A verbal representation is a problem

statement or re-statement using words.

! Apictorial representation includes motion

diagrams, coordinate systems, simple drawings, and symbols.

! A graphical representation uses graphs when appropriate.

! A mathematical representation uses specific equations which mustbe solved.

Solving Problems in Physics

Slide 1-70

Tactics: Drawing a Pictorial Representation


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ac cs a g a c o a ep ese a o

Slide 1-71

Tactics: Drawing a Pictorial Representation


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g p

Slide 1-72

General Problem-Solving Strategy


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g gy

Slide 1-73

Example 1.9 Launching a Weather Rocket


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p g

Slide 1-74



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p g

Slide 1-75



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p g

Slide 1-76



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p g

Slide 1-77

Units


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! Science is based on experimental measurements,and measurements require units.

!

The system of units in science is called le SystmeInternationale dunits or SI units.

! The SI unit of time is thesecond, abbreviated s.

! 1 s is defined as the timerequired for 9,192,631,770oscillations of the radio waveabsorbed 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 avacuum during 1/299,292,458 of a second.

Slide 1-78

An atomic clock at the National Institute ofStandards and Technology is the primarystandard of time.

Units


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! The SI unit of mass is thekilogram, abbreviated kg.

!

1 kg is defined as the mass ofthe international standardkilogram, a polished platinum-iridium cylinder stored in Paris.

!

Many lengths, times, andmasses are either much less ormuch greater than thestandards of 1 m, 1 s, and 1 kg.

! We use prefixes to denote

various powers of 10, whichmake it easier to talk aboutquantities.

Slide 1-79

Unit Conversions


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! It is important to be able toconvert back and forth between

SI units and other units.

! One effective method isto write the conversionfactor as a ratio equal to one.

! Because multiplying by 1 doesnot change a value, these ratiosare easily used for unit conversions.

!

For example, to convert the length 2.00 feet tometers, use the ratio:

! So that:

Slide 1-80

Assessment


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! When problem solving, it is important to decide whether ornot your final answer makes sense.

!

For example, if you are working aproblem about automobile speedsand reach an answer of35 m/s, is this a realistic speed?

!

The table shows some approximateconversion factors that can be usedto 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 youmade a calculation error.

Slide 1-81

Significant Figures


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! 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 beenrounded 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 linkrule: The input value

with the smallest number of significant figures determinesthe number of significant figures to use in reporting the

output value.

Slide 1-82


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2013 Pearson Education, Inc. Slide 1-83

Determining significant figures.

Tactics: Using Significant Figures


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EXAMPLE 1.10 Using significant figures


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Orders of Magnitude and Estimating


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! In many cases a very

rough estimate of anumber is sufficient.

! A one-significant-figureestimate or calculation

is called an order-of-magnitude estimate.

! An order-of-magnitudeestimate is indicated by

the symbol ~, whichindicates even lessprecision than ".

Slide 1-86

Some approximate lengths and masses

Distance you can drive in 1 hour ~105m

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 ~104m

Small car ~1000 kg

Large human ~100 kg

Science textbook ~1 kg

Apple ~0.1 kg

Raisin ~103kg

QuickCheck 1.11


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Rank in order, from the most to the least, the number of

significant figures in the following numbers. For example, ifb has more than c, c has the same number as a, and a hasmore than d, you would give your answer as b > c = a > d.

a. 8200 b. 0.0052 c. 0.430 d. 4.321 #1010

A.

d > c > b = a

B.

a = b = d > c

C.

b = d > c > a

D.

d > c > a > b

E.

a = d > c > b

Slide 1-87

QuickCheck 1.11


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Rank in order, from the most to the least, the number of

significant figures in the following numbers. For example, ifb has more than c, c has the same number as a, and a hasmore than d, you would give your answer as b > c = a > d.

a. 8200 b. 0.0052 c. 0.430 d. 4.321 #1010

A. d > c > b = a

B.

a = b = d > c

C.

b = d > c > a

D.

d > c > a > b

E.

a = d > c > b

Slide 1-88

2? Ambiguous 2 43


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Chapter 1 Summary Slides

Slide 1-89

General Strategy


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General Strategy


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Important Concepts


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Important Concepts


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lecture 1 - physics

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