Chapter 1Chapter 1

Introduction

• A good understanding of geometry and trigonometry will help solve almost all the problems involved in this course.

• Physics like all other sciences is data driven. Thus, it is vital that _______________ are collected and recorded correctly.

• ________ allow us to take a large amount of data and analyze them for any patterns. Graphs are also useful predictive tools.

Mathematics and Physics • Physics is relevant to much in our daily lives.

a) Many of the _________________ that we take for granted would not exists without physics.

• Physics is the most ______________ science. a) It serves as a ____________ on which the

physical sciences are based.

b) __________ found in physics are also used in the life sciences.

• Physics takes our known and unknown world and tries to explain them in terms of some basic principles.

Mathematics and Physics

• In physics ________________are used as tools to model observations and make predictions.

EQUATIONS

• Thus, knowing how to interpret and use an equation is vital to learning physics.

Modeling observations

Making predictions

Sample Problem

The potential difference, or voltage (V), across a circuit equals the current (I) multiplied by the resistance (R) in the circuit. That is, V=I x R. What is the resistance of a light bulb that has a 0.75 ampres current when plugged into a 120-volt outlet?

Mathematics and Physics

• When working through problems always check to make sure that the final answer makes sense. (i.e. if you are calculating for the mass of a planet and you get 50 kg. this should raise concerns).

• One way to check if an answer is correct is by analyzing the units using _____________ (more on this in a moment).

Mathematics and Physics

• In physics, and the sciences in general, the ______________of units are used to measure physical quantities such as length, mass, time, etc.a) SI = “Systeme International d’Unites”

• There are ___________ base SI quantities (see Table1-1, p.5 for a list).a) Other units are derived from these base units

and orders of magnitude can be changed by using the Greek prefixes.

Mathematics and Physics • ____________________is a method of doing

algebra with units.

• Dimensional analysis is a powerful tool for solving problems.

• We can use dimensional analysis for:a) ______________________

b) _____________ to see if the formula we are using and our answer are correct

• We will be using dimensional analysis for

both purposes.

Mathematics and Physics • Using dimensional analysis to determine if the

formula we are using and the answer we get are correct requires us to examine the ____________________________________.

• We start by analyzing the “dimensions” involved in the measurements.a) Dimension: The physical nature of a quantity.

Ex.) the distance between two points can be measured in feet, meter, inches, etc. But the dimension describing this distance is “length.”

Mathematics and Physics • We can treat these dimensions as

__________ expressions.a) Dimensions for length, mass, and time are L, M,

and T.

b) Using these abbreviations we can analyze a formula .

• In this process any number in the formula should be _____________.

• Brackets ([ ]) indicates “the dimensions of a physical quantity”a) [V] = the dimensions of volume.

Sample ProblemVolume = distance3 so [V] = ?

Density = _mass__ so [D] = ?

Volume

 

Velocity (speed) = distance so [v] = ?

time

 

Acceleration = velocity so [a] = ?

time

 

Sample Problem Show that the following expression is dimensionally correct.

x = vt + ½ at2

Show that the following expression is dimensionally incorrect.

x2 = ½ a2t

Mathematics and Physics • To use dimensional analysis to do conversions we

need to remember what conversion factors are and how to use them.

• Conversions factors: multipliers that are equal to _________ and are used as fractions to cancel some “unwanted” unit and obtain the “wanted” unit. Because 1000m = 1 km

1000 m = 1 or 1 km = 1

1 km 1000 m

• The “conversion” is then simply a _______________ problem involving factions.

Sample Problem How many meters is 43 km?

Mathematics and Physics • Significant digits (SD) are all the “valid” digits

of a measurement.a) Valid digits = all certain + one estimated

digits digit

• The number of _______________indicate the precision (not accuracy) of the measurement.

• The number of SD’s in a measurement is dependent on the smallest unit on the measuring device.

• The one estimated digit is the one farthest

to the right.

Mathematics and Physics • Significant digit review:

a) All nonzero digits are __________ .

b) Any zeros between nonzero digits are _________.

c) All leading zeros are _____________.

d) Trailing zeros when a decimal point is present are __________.

e) Counted quantities and conversion factors have an __________ number of significant digits.

Mathematics and Physics • Significant digit review: Adding/subtracting

a) The value with the least number of _______________ determine how many decimal places we can have in the answer and thus the number of significant digits.

• Significant digit review: Multiplying/dividinga) The value that has the least number of

_________________in the problem determines how many significant digits we can have in the answer.

Mathematics and Physics • Significant digits review: Rounding

a) Left most digit < 5

Drop all digits that follow and the last digit to be kept remains the same.

b) Left most digit > 5

Drop all digits that follow and the last digit to be kept is increased by one.

Mathematics and Physics • The _____________________involves making

observations, doing experiments, and creating models or theories to explain the results or predict new answers.a) ______________: An idea, equation, structure, or system

used to describe a phenomenon. New data can either support or force a reexamination of the model.

b) _______________: A rule of nature that sums up related observations to describe a pattern in nature.

c) _______________: An explanation based on many observations supported by experimental results.

Measurements

• Measurements __________ our observations.

• The standards are the SI units as determined by a given calibrated measuring device.

• Measurements are always reported with an uncertainty.a) The uncertainty value allows us to compare

results .

A measurement is defined as a comparison between an unknown quantity and a standard.

Measurements

• ____________________are two characteristic traits of any measured value.a) Remember these are not the same.

• _______________: the degree of exactness of a measurement.

• _______________: Describes how well the results of a measurement agree with the “real” or accepted value as measured by a competent experimenter.

Graphing Data

• Graphs are very useful tools. They allow us to ____________________in a series of data.

• Generating a useful graph starts with insuring that the data is collected in a consistent manner.

• Plotting the data points on a graph and generating a line of best fit allows us to make extrapolative and interpolative predictions.

Graphing Data• Constructing a graph requires the selection of

a coordinate system to locate data points on the graph.a) Two commonly used ____________________in

physics are the Cartesian (rectangular) and the plane polar.

Graphing Data• Construction of a good graph also requires the

collection of good, consistent data.

• That means when conducting an experiment it is important that only one factor is _________ at a time.a) ________________: Any factor that might affect

the behavior of an experimental setup.

b) ________________: The factor that changes as a result of an alteration in another factor.

c) ________________: The factor that is changed or manipulated during an experiment.

Graphing Data• The _______________is a line that is a line drawn to

as close to all the data points as possible.

This line can be used to make_____________ by extrapolation or interpolation.

Graphing Data

• The different curves obtained as a result of plotting the data on a graph suggests different relationships.

• There are different relations that can be derived. The three we will talk about are:• Linear• Quadratic• Inverse

Graphing Data• __________________: The two variables vary

linearly with one another.

• The equation expressing this relationship is:

y = mx + b

The slope of this line is positive.What would a negative slope look like?

Graphing Data• _____________________: One variable depends

on the square of another.• The equation expressing this relationship is:

y = ax2 + bx + c

These graphs take the shape of a _____________.

Graphing Data• _________________: One variable depends

on the inverse of the other.• The equation expressing this relationship is:

y = a/x

These graphs also take the shape of a _______________.

Chapter 1Chapter 1

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