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• FOR SCIENTISTS AND ENGINEERS

physics a strategic approach THIRD EDITION

randall d. knight

2013 Pearson Education, Inc.

Chapter 1 Lecture

• SI Quantities & Units In mechanics, three basic quantities are used

Length, Mass, Time Will also use derived quantities

Ex: Joule, Newton, etc. SI Systme International

agreed to in 1960 by an international committee

• Density: A derived Quantity

Density is an example of a derived quantity It is defined as mass per unit volume Units are kg/m3

mV

• Length: METER

The meter is defined to be the distance light travels through a vacuum in exactly 1/299792458

seconds. 1 m is about 39.37 inches. I inch is about 2.54 cm.

• Powers of Ten!

• Mass: Kilogram Units

SI kilogram, kg Defined in terms of a

kilogram, based on a specific cylinder kept at the International Bureau of Standards

Mass is Energy! (Physcis 43)

• Time: Second

Units seconds, s

Defined in terms of the oscillation of radiation from a cesium atom

• Prefixes

The prefixes can be used with any base units

They are multipliers of the base unit

Examples: 1 mm = 10-3 m 1 mg = 10-3 g

• To convert from one unit to another, multiply by conversion factors that are equal to one.

• To convert from one unit to another, multiply by conversion factors that are equal to one.

Example: 32 km = ? nm 1. 1km = 103 m 2 1 nm = 10-9 m

3 910 10321 1

m nmkmkm m

3 932 10 10 nm= 133.2 10 nm=

• 1 light year = 9.46 x 1015m 1 mile = 1.6 km

How many miles in a light year?

15

3

9.46 10 111 1.6 10

m milelyly m

125.9 10 miles=

• 1 light year = 9.46 x 1015m 1 mile = 1.6 km

~ 6 Trillion Miles!!! Closest Star: Proxima Centauri 4.3 ly Closest Galaxy: Andromeda Galaxy 2.2 million ly

• It had long been known that Andromeda is rushing towards Earth at about 250,000 miles per hour -- or about the distance from Earth to the moon. They will collide in 4 billion years!

• Significant Figures

A significant figure is one that is reliably known

Zeros may or may not be significant Those used to position the decimal point are not

significant To remove ambiguity, use scientific notation

In a measurement, the significant figures include the first estimated digit

• Significant Figures, examples

0.0075 m has 2 significant figures The leading zeros are placeholders only Can write in scientific notation to show more clearly:

7.5 x 10-3 m for 2 significant figures 10.0 m has 3 significant figures

The decimal point gives information about the reliability of the measurement

1500 m is ambiguous Use 1.5 x 103 m for 2 significant figures Use 1.50 x 103 m for 3 significant figures Use 1.500 x 103 m for 4 significant figures

• Sig Fis & Scientific Notation

• Rounding

Last retained digit is increased by 1 if the last digit dropped is 5 or above

Last retained digit remains as it is if the last digit dropped is less than 5

Saving rounding until the final result will help eliminate accumulation of errors

Keep a few extra terms for intermediate calculations

• Round Each to 3 Sig Figs

124.65 0.003255 12.25 3675

• Plate Problem

A rectangular plate has a length of 21.3 cm and a width of 9.8 cm. Calculate the area of the plate, and the number of significant figures.

A = 21.3cm x 9.8cm = 208.74cm2

A = 210cm2

How many significant figures? 2

• Operations with Significant Figures Multiplying or Dividing

When multiplying or dividing, the number of significant figures in the final answer is the same as the number of significant figures in the quantity having the lowest number of significant figures.

Example: 25.57 m x 2.45 m = 62.6465 m2 The 2.45 m limits your result to 3 significant

figures: 62.6m2

• Operations with Significant Figures Adding or Subtracting

When adding or subtracting, the number of decimal places in the result should equal the smallest number of decimal places in any term in the sum.

Example: 135 cm + 3.25 cm = 138 cm The 135 cm limits your answer to the units

decimal value

• Operations With Significant Figures Summary

The rule for addition and subtraction are different than the rule for multiplication and division

For adding and subtracting, the number of decimal places is the important consideration

For multiplying and dividing, the number of significant figures is the important consideration

• 2013 Pearson Education, Inc.

Chapter Goal: To introduce the fundamental concepts of motion.

Chapter 1 Concepts of Motion

Slide 1-2

Pickup PSE3e Photo from page 2, snowboarder jump.

• 2013 Pearson Education, Inc.

Chapter 1 Preview

Slide 1-3

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Chapter 1 Preview

Slide 1-4

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Chapter 1 Content, Examples, and QuickCheck Questions

Slide 1-18

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Four basic types of motion Slide 1-19

• 2013 Pearson Education, Inc.

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.

Making a Motion Diagram

Slide 1-20

• 2013 Pearson Education, Inc.

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

• 2013 Pearson Education, Inc.

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.

Examples of Motion Diagrams

Slide 1-22

• 2013 Pearson Education, Inc.

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.

Examples of Motion Diagrams

Slide 1-23

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Example: A jump shot from center court. In this case the ball is

slowing down as it rises, and speeding up as it falls.

Examples of Motion Diagrams

Slide 1-24

• 2013 Pearson Education, Inc.

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 were concentrated 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

• 2013 Pearson Education, Inc.

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.

Position and Time

Slide 1-31

• 2013 Pearson Education, Inc.

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

• 2013 Pearson Education, Inc.

Slide 1-33

• 2013 Pearson Education, Inc.

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 .