Chapter 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 Problem Volume = distance 3 so[V] = ? Density = _mass__so[D] = ? Volume Velocity (speed) = distanceso[v] = ? time Acceleration = velocityso[a] = ? time

Sample Problem Show that the following expression is dimensionally correct. x = vt + ½ at 2 Show that the following expression is dimensionally incorrect. x 2 = ½ a 2 t

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/dividing a)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 = ax 2 + 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 1 The End