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Honors Physics

A Physics Toolkit

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Honors Physics Chapter 1

Turn in Contract/Signature Lecture: A Physics Toolkit Q&A Website: http://www.mrlee.altervista.org

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The Metric System

Physics is based on measurement. International System of Units (SI unit)

– Fundamental (base)quantities: more intuitive

– Derived quantities: can be described using fundamental quantities.

length, time, mass …

Speed = length / time Volume = length3

Density = mass / volume = mass / length3

Two kinds of quantities:

– Created by French scientists in 1795.

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Units

Unit: a measure of the quantity that is defined to be exactly 1.0.

Fundamental (base) Unit: unit associated with a fundamental quantity

Derived Unit: unit associated with a derived quantity

– Combination of fundamental units

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Units

Standard Unit: a unit recognized and accepted by all.

Quantity Unit Name Unit Symbol

Length Meter m

Time Second s

Mass kilogram kg

Some SI standard base units

– Standard and non-standard are separate from fundamental and derived.

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Prefixes Used With SI Units

Prefix Symbol Fractions

nano n 10-9

micro 10-6

milli m 10-3

centi c 10-2

kilo k 103

mega M 106

giga G 109

61 1 10m m 31 1 10mm m

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Conversion Factors

1 m = 100 cmso

1100

1

cm

mand 1

1

100

m

cm

Conversion factor:cm

m

100

1or

m

cm

1

100

Which conversion factor to use?

Depends on what we want to cancel.

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Example

2.1 km = ____ m

2.1 2.1km km Not good, cannot cancel

2.1 2.1km km

Given: 1 km = 1000 m

1

1000

km

m

1000

1

m

km32100 2.1 10m m

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Practice

12 cm = ____ m

112 12 0.12

100

mcm cm m

cm

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Chain Conversion

1.1 cm = ___ km

1.1 1.1cm cm 1

1000

km

m 51.1 10 km

1 1000

1 100

km m

m cm

100

m

cm

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Practice

7.1 km = ____ cm

51000 1007.1 7.1 7.1 10

1 1

m cmkm km cm

km m

1 1000

1 100

km m

m cm

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Still simple? How about…

2 mile/hr = __ m/s

Chain Conversion

2 2mile mile

hr hr 1600m

mile

1

3600

hr

s

0.89m

s

1 3600

1 1600

hr s

mile m

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When reading the scale,

Estimate to 1/10th of the smallest division

1 1 cm.5

1.3 cm

– Draw mental 1/10 divisions– However, if smallest division is already too small,

just estimate to closest smallest division.

but not 1.33 cm, why?

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Uncertainty of Measurement

All measurements are subject to uncertainties. External influences: temperature, magnetic field Parallax: the apparent shift in the position of an object when

viewed from different angles.

Uncertainties in measurement cannot be avoided, although we can make it very small by using good experimental skills and apparatus.

Uncertainties are not mistakes; mistakes can be avoided.

Uncertainty = experimental error

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Precision

Precision: the degree of exactness to which a measurement can be reproduced.

The precision of an instrument is limited by the smallest division on the measurement scale.

Smaller uncertainty = more precise Larger Uncertainty = less precise

– Uncertainty is one-tenth of the smallest division. Typical meter stick: Smallest division is 1 mm = 0.001 m,

uncertainty is 0.1 mm = 0.0001m.

– A typical meterstick can give a measurement of 0.2345 m, with an uncertainty of 0.0001 m.

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Accuracy

Accuracy: how close the measurement is to the accepted or true value

Accuracy Precision

Accepted (true) value is 1.00 m. Measurement #1 is 0.99 m, and Measurement #2 is 1.123 m.

– ____ is more accurate:#1

#2

closer to true value

– ____ is more precise: uncertainty of 0.001 m (compared to 0.01 m)

more precise more accurate

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Significant Figures (Digits)

1. Nonzero digits are always significant.2. The final zero is significant when there is a decimal

point.3. Zeros between two other significant digits are always

significant.4. Zeros used solely for spacing the decimal point are not

significant.

Example: 1.002300

0.004005600 7 sig. fig’s

7 sig. fig’s 12300 3 sig. fig’s

12300. 5 sig. fig’s

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Practice:

How many significant figures are there ina) 123000

b) 1.23000

c) 0.001230

d) 0.0120020

e) 1.0

f) 0.10

3

64

6

2

2

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Operation with measurements

In general, no final result should be “more precise” than the original data from which it was derived.

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Addition and subtraction with measurements

The sum or difference of two measurements is precise to the same number of digits after the decimal point as the one with the least number of digits after the decimal point.

Example:

16.26 + 4.2 = 20.46

Which number has the least digits after the DP? 4.2 Precise to how many digits after the DP? 1 So the final answer should be rounded-off (up or down) to how many digits after the DP? 1

=20.5

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Practice:

1) 23.109 + 2.13 = ____

2) 12.7 + 3.31 = ____

3) 12.7 + 3.35 = ____

4) 12. + 3.3= ____

1) 23.109 + 2.13 = 25.239 = 25.24

2) 12.7+3.31 = 16.01 = 16.0Must keep this 0.

3) 12.7+3.35 = 16.05 = 16.1

4) 12. + 3.3 = 15.3 = 15. Keep the decimal pt.

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Multiplication and Division with measurements

The product or quotient has the same number of significant digits as the measurement with the least number of significant digits.

Example:2.33 4.5 = 10.485

Which number has the least number of sig. figs? 4.5 How many sig figs does it have? 2 So the final answer should be rounded-off (up or down) to how many sig figs? 2

=10.

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Practice:

2.33/3.0 = ___

2.33 / 3.0 = 0.7766667 = 0.78

2 sig figs

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What about exact numbers?

Exact numbers have infinite number of sig. figs.

If 2 is an exact number, then 2.33 / 2 = __

2.33 / 2 = 1.165 = 1.17

Note: 2.33 has the least number of sig. figs: 3

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Scientific Notation

Whenever it becomes awkward to say a number, use scientific notation.

4 times to the left

4 times to the right

M 10n

Example:

1 <= |M| < 10 n: exponent (positive, zero, or negative integer)

23000 = 2.3 104

0.00032 = 3.2 10-4

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Practice

860000 = _________ 0.0000102 = ________ 30000000 = ________ 0.0000003 = ________

8.6 × 105

1.02 × 10-5

3 × 107

3 × 10-7

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Arithmetic Operations in Scientific Notation

Adding and subtracting with like exponents Adding and subtracting with unlike exponents Adding and subtracting with unlike units Multiplication using scientific notation Division using scientific notation

Use calculator.

Skip to Slide 36

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Adding and subtracting with like exponents

Add or subtract the values of M and keep the same n.

Example:2 105 m + 3 105 m

= (2 + 3) 105 m = 5 105 m

5.3 104 m – 2.1 104 m = (5.3 – 2.1) 104 m = 3.2 104 m

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Practice:

___106103 22 mm

2 2

2

2

3 10 6 10

3 6 10

9 10

m m

m

m

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Adding and subtracting with unlike exponents

1. First make the exponents the same.

2. Then add or subtract.

2.0 103 m + 5 102 m

= 2.0 103 m + 0.5 103 m

= (2.0 + 0.5) 103 m

= 2.5 103 m

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Practice:

___100.6103 76 mm

6 7

7 7

7

7

3 10 6.0 10

0.3 10 6.0 10

0.3 6.0 10

6.3 10

m m

m m

m

m

76

66

103.0101010

3

1010

103103

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Adding and subtracting with unlike units

1. Convert to common unit

2. Make the components the same

3. Add or subtract

Example:

2.10 m + 3 cm

= 2.10 m + 0.03 m

= 2.13 m

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Multiplication using scientific notation

1. Multiply the values of M

2. Add the exponents

3. Units are multiplied

(3 104 kg) (2 105 m)

= (3 2) 104+5 (kgm)

= 6 109 kg×m

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Practice:

___105102 53 mm

3 5 3 5

8 2

9 2

2 10 5 10 2 5 10

10 10

1 10

m m m m

m

m

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Division using scientific notation

1. Divide the values of M.

2. Subtract the exponent of the divisor from the exponent of the dividend.

3. Divide the unit of the divisor from the unit of the dividend.

66 ( 2) 8

2

6 10 610 2 10

3 10 3

m m mss s

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Displaying Data

Table Graph

Independent variable: manipulated Dependent variable: responding

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Table

Title or description Variables (quantities) Unit (either after variables or each value)

Table 1: Displacement and speed of cart at different times

Time (s) Displacement (m) Speed

1.0 2.4 2.4 m/s

2.1 4.9 2.3 m/s

3.1 7.6 2.2 cm/s

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Graph

Title or description Labels

Independent variable on horizontal axis Dependent variable on vertical axis

Units Scales

Horizontal and vertical can be different

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Graph Example

Velocity of falling block at different time

0

2

4

6

8

10

12

14

0 2 4 6 8Time (s)

Ve

loc

ity

(m

/s)

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Linear Relationship

m: slope

bmxy

12

12

xx

yym run

rise

b: y-intercept

x

y

x1

x2

y1

y2

b

Direct Relationship: y mx

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Inverse Relationship

Hyperbola

ay

x

0

1

2

3

4

5

6

0 1 2 3 4 5