Physics chapter 11 Models, Measurements, and Vectors.

Physics chapter 1 1

Models, Measurements,and Vectors

Physics chapter 1 2

Physics is….

The study of nature. the study of the natures of matter and

energy. The study of the relationship between

matter and energy.

Physics chapter 1 3

Physics is based on

Experiments Observations

Physics chapter 1 4

The language of physics

The laws of physics can almost always be expressed using mathematical relationships.

So, mathematics is the language of physics.

Physics chapter 1 5

Why study physics?

A fundamental science

Technology

Scientific insight into everyday world

Physics chapter 1 6

Theories

Theories

Principles

Laws

Physics chapter 1 7

Idealized models

ModelSimplified version of a complicated physical

system

We neglect minor effects on the system to concentrate on the major effects.

Physics chapter 1 8

Units

We use the metric or SI system Base units

Meter – m – lengthKilogram – kg – massSecond – s – time

All answers must have units, or they are meaningless

Physics chapter 1 9

Prefixes

Added to units to indicate mulitples of 10 or 1/10

Kilo – 1000 or 103 – kilometer – km Nano – 10-9 – nanosecond – ns Milli – 10-3 – milligram – mg Micro – 10-6 – microsecond – ms Page 6 for more

Physics chapter 1 10

Unit analysis

Also called dimensional analysis. Units must work out. Units are treated just like algebraic

symbols in equations


Example 1

vtd

km/h 100v h 2t

h 2h

km100

d

km 200d


Alternative method (Example 2)

vtd

km/h 100v h 2t

2002100 d

km 200d

kmhh

km


Unit Conversions

Use ratios

Carry your units through to make sure they cancel


Example 3

Convert 6 ft 1 in to m.


Uncertainty

More accurate measurements have less uncertainty.

We can express uncertainty in two ways:75.6 3.78 cm75.6 cm 5%


Significant figures

We usually don’t write numbers with uncertainties.

Instead, we use significant figures.


Significant Figures

All the digits known in a measurement, plus one that is somewhat uncertain.

All nonzero digits are significant Zeros are governed by four rules

1. Zeros between nonzero digits are significant

203 has 3 sig figs 5.0279 has 5 sig figs


Significant Figures

2. Zeros in front of all nonzero digits are not significant

0.0035 has 2 sig figs 0.0008 has 1 sig fig

3. Zeros at the end of a number and after the decimal point are significant.

75.000 has 5 sig figs 0.000800 has 3 sig figs


Significant Figures

4. Zeros at the end of a number but before the decimal point may or may not be significant.

If a zero is just a placeholder, it is not significant. If it has been measured, it is significant. To show

all zeros are significant, use a decimal point. To show some are, use scientific notation (later) 2000 has 1 sig fig 2000. has 4 sig figs


Examples 4

2.52 sig figs

2.503 sig figs

2502 sig figs

250.3 sig figs

250.04 sig figs

0.00252 sig figs

0.002503 sig figs

0.0025014 sig figs


Multiplication and Division

The result should have the same number of significant figures as the least number of significant figures in any factor.


Example 5

Since 1.2 only has 2 sig figs, our answer can only have 2 sig figs. We would record our answer as 1.6

608.12.134.1


Example 6

Since 8 only has 1 sig fig, the answer should only have 1 sig fig. Record the answer as 3

25.38

26


Addition and Subtraction

The result has no significant figures beyond the last decimal place where all of the original numbers had significant figures.


Example 7

Since 1.040 only has 3 sig figs after the decimal, the answer can only have 3 sig figs after the decimal. Record the answer as 1.253

25342.1

21342.0

040.1


Example 8

Since 900 has its last sig fig in the hundreds column, then the result’s last sig fig must be in the hundreds column. Record the answer as 300

340

900

1240


Conversion factors

Conversion factors are considered exact, and do not affect significant digits.

There are exactly 100 cm in 1 m, so don’t use the 100 to figure out how many significant digits your answer should have.


Scientific Notation

Useful when writing very small or very large numbers

Also useful for indicating the number of significant figures

696,000,000 m = 6.96 x 108 m 4,000,000 km = 4 x 106 km

or 4.00 x 106 km


Precision vs. Accuracy

Bathroom scale with 5 pound increments might be very accurate, but is not very precise.

Doctor’s office scale with 1/10 pound increments is very precise, but might not be very accurate.

A good measurement is both accurate and precise.


Estimates and orders of magnitude Read section 1.6, including the example.


Vectors

Have magnitude and direction Typed in bold with an arrow over them

A

Handwritten with an arrow over them


Vectors

Two vectors with the same direction are parallel.

Two vectors with the opposite direction are antiparallel.

Two vectors with the same direction and magnitude are equal.


Vector magnitude

The magnitude of a vector is a scalar (a number) and is always positive.

Write it as the vector name without the arrow or like this:

A


Vector addition - geometrically

Place the tail of the second vector at the tip of the first vector.

The vector sum, or the resultant, is the vector connecting the starting point and the ending point.


Example 9

Miss Becker drives 4 mi north and then 11 mi west. How far and in what direction is she from her starting point?


Vector subtraction

Just flip around vector B and then add.

BABA


Vector components

Any vector can be separated into component vectors that are parallel to the Cartesian (x and y) axes.

The vector sum of these components is equal to the original vector

yx AAA


Finding vector components

We can find vector components using trigonometry.

A

yA

xA

y

x cosAAx sinAAy

A

AxcosA

Aysin

These equations work when q is measured CCW from the positive x-axis.


Example 10

B

yB

xB

y

x

m 0.5B 50

cosBBy

B

BycosB

Bxsin

sinBBx

50cosm 0.5yB 50sinm 0.5xB

m 2.3yB m 8.3xB


Vector addition – using components Each component of the resultant vector is

equal to the sum of the corresponding components of the vectors being added

... xxxx CBAR

... yyyy CBAR


Finding vector magnitude and direction If given a vector in terms of its

components, we can find its magnitude and direction using trig

m 4.1

m 1.6

y

x

A

A

A

yA

xA

y

x

22yx AA A

22 m 4.1m 6.1 A

2m 52.4A

m 1.2A


Finding vector direction

A

yA

xA

y

x

x

y

A

Atan

x

y

A

A1tan

m 6.1

m 4.1tan 1 41


Example 11

Find the resultant vector in terms ofA) componentsB) magnitude and direction

BAR

m 4.1

m 8.4

y

x

A

A

m 83

m 3.2

.B

B

y

x


Example part A)

yyy

xxx

BAR

BAR

m 6.1xR

m 4.2yR

m 2.3m 8.4 xR

m 8.3m 4.1 yR


Example part B)

22yx RR R

22 m 4.2m 6.1 R

m 9.2R


Example part B)

Is this right?

x

y

R

R1tan 1 2.4 mtan

1.6 m

56


Tan-1 can be tricky

Angles that differ by 180° have the same tangent.

Your calculator doesn’t know which one you want.

R

56 180 236 y

x

axis- xnegative fromCCW 56

or56

56

Physics chapter 11 Models, Measurements, and Vectors.

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Transcript of Physics chapter 11 Models, Measurements, and Vectors.