Mathematics and Physics

Physics is a branch of science that involves the study of the physical world: energy, matter, and how they are related.

What is Physics?

Section

1.1

Learning physics will help you to understand the physical world.

Any problem that deals with temperature, size, motion, position, shape or color involves physics.

Areas within Physics:Name Subject Example

Mechanics Motion Friction, falling objects, spinning objects

Thermodynamics Heat, temp Melting, freezing, engines, refrigerators

Waves Repetitive motion

Springs, pendulums, sound

Areas within PhysicsOptics Light Mirrors, lenses,

color

Electromagnetism Electricity, magnetism, light

Circuitry, electric charges

Relativity Particles moving at different speeds

Particle collisions, nuclear energy

Quantum Mechanics

Particle behavior

Atom and its parts

Review Questions:

• 1. Identify the area of physics that is most relevant to each of the following situations. Explain your reasoning.– A. High school football game– B. Food preparation for the prom– C. Playing in the school band– D. Lightning in a thunderstorm– E. Wearing sunglasses outside in the sun

Question #1 Answer

– A. High school football game: mechanics– B. Food preparation for the prom:

thermodynamics– C. Playing in the school band: waves– D. Lightning in a thunderstorm:

electromagnetism– E. Wearing sunglasses outside in the sun:

optics

Question #2

• Identify the area of physics involved in each of the following tests of a lightweight metal alloy proposed for use in sailboat hulls:

• A. Testing the effects of a collision on the alloy

• B. Testing the effects of extreme heat and cold on the alloy

• C. Testing whether the alloy can affect a magnetic compass needle

Answer #2

• A. Testing the effects of a collision on the alloy: mechanics

• B. Testing the effects of extreme heat and cold on the alloy: thermodynamics

• C. Testing whether the alloy can affect a magnetic compass needle: electromagnetism

Mathematics and Physics

The Système International d’Unités, or SI, uses seven base quantities, which are shown in the table below.

SI Units

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1.1

Measurement

Derived units• Area – square meter, m2

• Volume – cubic meter, m3

• Force – newton, N• Pressure – pascal, Pa• Energy – joule, J• Power – watt, W• Voltage – volt, V• Frequency – hertz, Hz• Electric charge – coulomb, C

Mathematics and Physics

Measuring standards for kilogram and meter are shown below.

International Bureau of Weights and Measures in Sèvres, France and the National Institute of Science and Technology (NIST) in Gaithersburg, Maryland

http://www.surveyhistory.org/the_standard_meter1.htm

SI Units

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1.1

Metric PrefixesPrefix Symbol Multiple of

base unit

giga- G 109

mega- M 106

kilo- k 103

hecto- h 102

deka- da 101

deci- d 10-1

centi- c 10-2

milli- m 10-3

Metric Prefixes (cont)Prefix Abbreviation Multiple of

Base Unit

micro- µ 10-6

nano- n 10-9

Mnemonic device for remembering prefixes

• Great (giga)• Magnificent

(mega)• King (kilo)• Hector (hecto)• Drinks (deka)

• Ultra (unit)• Delicious (deci)• Chocolate (centi)• Milk (milli)• Most (micro)• Nights (nano)

Conversion practice

• 1. 30 Gm = ___ µm• 2. 1 Mg = ___ ng• 3. 0.052 mL = ___ ML• 4. 0.58 Mm = ___ nm• 5. 597 ng= ____ mg

Mathematics and Physics

This method of treating the units as algebraic quantities, which can be cancelled, is called dimensional analysis.

Dimensional analysis also is used in choosing conversion factors.

A conversion factor is a multiplier equal to 1. For example, because 1 kg = 1000 g, you can construct the following conversion factors:

Dimensional Analysis

Section

1.1

g 1000kg 11 kg 1

g 10001

Section Check

The potential energy, PE, of a body of mass, m, raised to a height, h, is expressed mathematically as PE = mgh, where g is the gravitational constant. If m is measured in kg, g in m/s2, h in m, and PE in joules, then what is 1 joule described in base unit?

Question 1

Section

1.1

A. 1 kg·m/s

B. 1 kg·m/s2

C. 1 kg·m2/s

D. 1 kg·m2/s2

Section Check

Answer: D

Answer 1

Reason:

Section

1.1

2m

1J = 1kgs

2

m1J = 1kg m

s

PE mgh

Section Check

A car is moving at a speed of 90 km/h. What is the speed of the car in m/s? (Hint: Use Dimensional Analysis)

Question 2

Section

1.1

A. 2.5×101 m/s

B. 1.5×103 m/s

C. 2.5 m/s

D. 1.5×102 m/s

Section Check

Answer: A

Answer 2

Reason:

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1.1

90 km 1000 m 1 h 1 min 25 m/s1 h 1 km 60 min 60 s

Section Check

Which of the following representations is correct when you solve 0.030 kg + 3333 g using scientific notation?

Question 3

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1.1

A. 3.4×103 g

B. 3.36×103 g

C. 3×103 g

D. 3363 g

Section Check

Answer: A

Answer 3

Section

1.1

Reason: 0.030 kg can be written as 3.0 101 g which has 2 significant digits, the number 3 and the zero after 3.

In number 3333 all the four 3’s are significant hence it has 4 significant digits. So our answer should contain 2 significant digits.

Mathematics and Physics

A meterstick is used to measure a pen and the measurement is recorded as 14.3 cm.

This measurement has three valid digits: two you are sure of, and one you estimated.

The valid digits in a measurement are called significant digits.

Significant Digits

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1.1

However, the last digit given for any measurement is the uncertain digit.

Mathematics and Physics

Observe (this may lead to or be the result of a question)

A scientist often works with an idea that can be worded as a hypothesis, which is an educated guess about how variables are related.

• Test with an experiment (record & analyze all data)

• Draw a conclusion from experiment (may lead to new hypothesis & more experiments)

Scientific Methods

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1.1

Mathematics and Physics

A scientific law is a rule of nature that sums up related observations to describe a pattern in nature.

A scientific theory is an explanation based on many observations supported by experimental results.

Models, Laws, and Theories

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1.1

Graphing Data

Identifying Variables

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1.3

The independent variable is the factor that is changed or manipulated during the experiment. (x axis)

The dependent variable is the factor that depends on the independent variable. (y axis)

Graphing Data

When the line of best fit is a straight line, the dependent variable varies linearly with the independent variable.

Linear Relationships

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1.3

xy

runrise

mΔΔ

Slope

Graphing Data

Nonlinear Relationships: Quadratic Relationship

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1.3

A quadratic relationship exists when one variable depends on the square of another.

Graphing Data

Nonlinear Relationships: Inverse Relationship

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1.3

In an inverse relationship, a hyperbola results when one variable depends on the inverse of the other.

Which type of relationship is shown following graph?

Question 1

Section

1.3 Section Check

A. Linear

B. Inverse

C. Parabolic

D. Quadratic

Section Check

Answer: B

Answer 1

Section

1.3

Reason: In an inverse relationship a hyperbola results when one variable depends on the inverse of the other.

Section Check

What is line of best fit?

Question 2

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1.3

A. The line joining the first and last data points in a graph.

B. The line joining the two center-most data points in a graph.

C. The line drawn close to all data points as possible.

D. The line joining the maximum data points in a graph.

Section Check

Answer: C

Answer 2

Section

1.3

Reason: The line drawn closer to all data points as possible, is called a line of best fit. The line of best fit is a better model for predictions than any one or two points that help to determine the line.