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FOR SCIENTISTS AND ENGINEERS

physics a strategic approach THIRD EDITION

randall d. knight

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 – Systéme 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

ρ ≡

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.

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?

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

Chapter Goal: To introduce the fundamental concepts of motion.

Chapter 1 Concepts of Motion

Pickup PSE3e Photo from page 2, snowboarder jump.

Chapter 1 Preview

Chapter 1 Content, Examples, and QuickCheck Questions

Four basic types of motion Slide 1-19

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

Cut individual frames of the filmstrip apart. Stack them on top of each other. This composite photo shows an object’s position at

several equally spaced instants of time. This is called a motion diagram.

Making a Motion Diagram

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

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.

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.

Often motion of the object as a whole is not influenced by details of the object’s 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

Motion diagram of a rocket launch

The Particle Model

Motion Diagram in which the object is represented as a particle

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 ball’s position in frame 4 can be specified with coordinates (x4, y4) = (12 m, 9 m) at time t4 = 2.0 s.

Position and Time

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

Tactics: Vector Addition

Sam’s 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 .

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 Sam’s change of position?

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

The negative of a vector.

Tactics: Vector Subtraction

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.

Time Interval

A stopwatch is used to measure a time interval.

It’s 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.

To quantify an object’s 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:

Average Speed, Average Velocity

The victory goes to the runner with the highest average speed.

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

EXAMPLE 1.2 Accelerating Up a Hill

Motion diagram of a car accelerating up a hill.

Sometimes an object’s velocity is constant as it moves. More often, an object’s 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

The Audi TT accelerates from 0 to 60 mph in 6 s.

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.

Tactics: Finding the Acceleration Vector

The Complete Motion Diagram

Example 1.5 Skiing Through the Woods

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 object’s 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.

Speeding Up or Slowing Down?

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

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 student’s motion.

Another way is to make a graph of x versus t for the student:

Position-versus-Time Graphs

Example 1.7 Interpreting a Position Graph

A new building requires careful planning. The architect’s visualization and drawings have to be complete before the detailed procedures of construction get under way. The same is true for solving 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 to create a representation, which is clear and precise.

A verbal representation is a problem statement or re-statement using words.

A pictorial representation includes motion diagrams, coordinate systems, simple drawings, and symbols.

A graphical representation uses graphs when appropriate.

A mathematical representation uses specific equations which must be solved.

Solving Problems in Physics

Tactics: Drawing a Pictorial Representation

General Problem-Solving Strategy

for scientists and engineers - santa rosa …srjcstaff.santarosa.edu/~lwillia2/40/40ch1_f14.pdffor...

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