# Introduction to Physics

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Introduction to Physics

What is Physics?  Physics is the study of how things work in terms of matter and energy at the most basic level. Physics is everywhere! Some areas of physics include: Thermodynamics Mechanics Vibrations and wave phenomena Optics Electromagnetism Relativity Quantum mechanics

Scientific Method Make an observation and collect data that leads to a question Formulate and objectively test hypotheses through experimentation Interpret the results and revise the hypotheses if necessary. State a conclusion in a form that can be evaluated by others.

Physicists use models to help build hypotheses , guide experimental design and help make predictions in new situations .

Sometimes the experiments don’t support the hypothesis
Sometimes the experiments don’t support the hypothesis. In this case the experiment is repeated over and over to be sure the results aren’t in error. If the unexpected results are confirmed, then hypothesis must be revised or abandoned. As a result the conclusion is very important. A conclusion is only valid if it can be verified by other people.

Keep in mind in that any theory, no matter how firmly it becomes entrenched within the scientific community, has limitations and at any point may be improved. ie. There is always a possibility that a new or better explanation can come along.

Problem Solving in Physics
In physics there is an organized approach that breaks down the task of obtaining information to solve a problem. List all the possible solutions Look for patterns Make a table, graph or figure Make a model Guess and check Work backwards Make a drawing Solve a simpler or similar related problem Often, the more problems you work on the better you get at solving them.

The Measure of Science Physics usually involves the measurement of quantities. In Physics, numerical measurements are different from numbers used in math class. In math, a number like 7 can stand alone and be used in equations. In science, measurements are more than just a number.

For example, if you were to measure your desk and report the measurement to be 150.
This leads to several questions: What quantity is being measured? What units was it being measured in? What did you used to measure it? How exact is the measurement?

SI Units – Base Units The system of measurement in the scientific community is the SI (Système International) is used. There are three fundamental units we will be using: seconds [s] to describe time kilograms [kg] to describe mass metres [m] to describe length

SI Units – Base Units

SI Units – Derived Units
Other units are found by combining these fundamental units: Example: volume = length x length x length = m3 speed = length ÷ time = m/s

Scientific Notation Often, the numbers we use are very large or very small so to make things easier, we use scientific notation The numerical part of the measurement must be between 1 and 10 and multiplied by a power of 10. Eg. A softball’s mass is about 180 g or 1.8 x 10-1g.

Prefixes We also use prefixes to accommodate these extreme numbers. Each prefix represents a power of 10.

Prefixes

Often we need to convert between units to solve a problem.
To convert between units we need to multiply by a factor of one.

We know that 1Mm = 106 m so: 1Mm = and m = 1 106 m Mm So how far is 652 Mm in m? (Pick the ratio that will cancel out the units)

Solution 652Mm x 106 m 1Mm =652 x 106 m =6.52 x 108 m

Sometimes you have to convert two units at once.
What is 200 km/h in m/s? Solution: * don’t forget that if you are adding two measurements, they must have the same units.

Accuracy and Precision
Accuracy is how close the measured value is to the true or accepted value. For example, when you read the volume of a liquid you will get a different measurement if you look at the meniscus from different angles. This phenomenon is called parallax

Problems with accuracy are due to error
Problems with accuracy are due to error. Experimental work is never free of error but it needs to be minimized. To minimize human error, parallax  should be minimized by taking the reading directly in front of the device being measured. Another way is to take several measurements to be made to be sure they are consistent.  Ex. Gas gauge, speedometer

Instrument error can also occur
Instrument error can also occur. This occurs when a device is not in good working  order. When lab equipment isn’t handled properly problems with accuracy arise.  Ex. Balances damaged, tare, wooden meter stick got wet etc…

Precision Precision is due to the limitation of the measuring device.
A microscope will give you a more precise picture of something small than a magnifying glass will. A ruler with mm on it will give you a more precise measurement than a ruler with only cm marks

When we are taking a measurement the last digit that we measure is estimated to a degree. In this course we will assume that you can make a fair estimate to about ½ of the smallest increment. For example, use a ruler to measure the length of your desk. What did you measure?

Was it exactly ? Might it have been closer to ? or perhaps been as small as ?

Because of the uncertainty in the last digit of your measuring device, we indicate that we are estimating our value to within ± ½ of the smallest increment. So your desk measurement would be We call this the measurement’s uncertainty.

Percent Error When you are taking measurements, the percent error is also important. To find the percent error in your measurements: |accepted value – measured value| x 100% accepted value

Significant Figures Numerically 3.0, 3.00, are of the same value, but shows that it was measured with the more precise instrument. The zeroes in all three numbers are considered "significant figures". They are shown to indicate the precision of the measurements. If we take away the zeroes, the value does not change. The measurement is still "three".

On the other hand, the zero in ". 03" is not a significant figure
On the other hand, the zero in ".03" is not a significant figure. It is important though, because if we leave it out and write .3 then the value is completely different from .03 (it is 10 times bigger). Thus, such zeroes are said to "place the decimal", and not considered "significant".

Sometimes. 03 is written as 0. 03
Sometimes .03 is written as The first zero also does not change the value of the number, but neither does it indicate more precision. It is generally included to stress the location of the decimal point, and its inclusion is never essential.

General Rules All digits are significant with the exception that:
1. leading zeroes are NOT significant ( has only one sig. fig.) 2. tailing zeroes in numbers without decimal points are ambiguous. (zeroes in 700 are not, but the zeroes in are) Such tailing zeroes are assumed not significant. They must be expressed in scientific notation to remove the ambiguity.

Example: 5200 as stated is assumed to have 2 sig. fig. If it were to have 3 sig. fig., it should have been expressed as 5.20 x 10 3. If it were to have 4 sig. fig., it should have been expressed as x 103,

Example: 30 is assumed to have one sig.fig. If you have to report such a number, you MUST express it in scientific notation.

30. has sig. fig. (The number has a decimal point, so all tailing zeroes are significant.) This is NOT appropriate notation. It also MUST be expressed in scientific notation.

30.0 has sig. fig. (Again, the number has a decimal point, so all tailing zeroes are significant.)

has sig. fig. (Leading zeroes are not significant, but the tailing zeroes are significant, because the number has a decimal point.)

12.00 has sig. fig. 32.0 x 102 has sig. fig.

Counting numbers and conversion numbers are always infinitely significant

Calculating with Significant Figures
When adding and subtracting with significant figures, the answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal.

Example: 97.3 +5.85  round off to 103.2

When multiplying or dividing the final answer must have the same number of significant figures as the measurement having the smallest number of significant figures. Example: 123 x 5.35  round off to 658

When adding or subtracting AND multiplying or dividing, you must keep track of your significant figures but save your rounding until the end.

Example 1: ( ) x 6.9 =12.65 x 6.9 =87.285 =87

Example 2: (4.2 – 4.18) x 19 = .02 x 19 = .38 = 0.4

Example 3: ( ) x 623 = 44.21X623 = =2.75X104

Example 4 =( ) x 3.12 =( ) x 3.12 =(.3921) x 3.12 = =1.2

Displaying Data

Displaying Data and Graphing
The best way to represent a set of data is by drawing a graph. We need to determine which variables are the independent variables and the dependent variables.

Independent variables are the ones we can manipulate (x axis)
Dependent variables are the ones that respond to the manipulation (y axis) We title the graph “y vs x”

Example: A car drives at a certain speed, brakes and travels a certain distance before it comes to a full stop. What are the two variables? distance and time Which is the independent and which is the dependent?   Independent: time Dependent: distance What would the title of this graph be? Distance vs Time

Rules for graphing: Independent variable goes on the x axis and the dependent goes on the y axis. Determine the range of both variables and label both axes accordingly. Use a ruler and use the whole space. Is the origin (0,0) a valid data point? Draw a best fit straight line or smooth curve ** do not do dot to dot** Give the graph a clear title that tells what it represents (dependent vs independent)

Let’s make a graph! Time (s) Volume (L) 7 1.0 28 2.0 60 3.0 86 4.0 114
7 1.0 28 2.0 60 3.0 86 4.0 114 5.0 138 6.0 175 7.0 200

Scaling your Axes: Scaling your Axes: On your graph paper you have a set number of division s for each axis. You proceed as follows to assign the value for each division: Division value = largest data - smallest data Number of divisions

Example: For time (x axis) we have _____ divisions and a range of 0s to 7.0s div. value = = s/div You have some leeway to round this value up to a convenient value, say, __________ s/div, but you cannot round it down (your data will not fit on the graph if you do). This method allows us to use the maximum spread of the graph paper, giving us a longer line and more accurate slope calculations.

For the volume data we have div value =
Do not use an awkward scale. The scale should be in easy counting numbers. Good numbers for scaling are 1, 2, 3 or multiples like 10, 20, 30 etc

Plotting the line Let the y intercept take care of itself.
Straight lines: set your ruler on the page a pass it through the line the data suggests, keeping equal numbers of dots above and below the line. Let the y intercept take care of itself.

Curved lines: Use your elbow as a pivot and ghost your pencil over the points, fine tuning your curve with your hand. When you have it right, put your pencil down and draw in the curve in one pass Make sure your graph has all the required parts as listed above.

Volume vs Distance Volume [L] Time [s]

Types of graphs: Linear Relationships
The dependent variable varies linearly with the independent variable in the form y = mx + b where b = y intercept or where the line crosses the y axis m = rise = Δy = yf - yi run Δx xf - xi

Quadratic Relationships (Parabolic) Smooth line curves upwards in the form y = kx2 where k = some constant

Inverse relationships (hyperbolic)
Smooth line curves downwards in the form: y = k ( ) = kx-1 1 x

Frequency and Period Time is an important measure of events in physics. There are two quantities that we can record that will give us a sense of time. Frequency Period

Frequency Frequency is the number of events that occur within a given amount of time (usually represented by f ) Example: The number of times a guitar string vibrates back and forth might be 300 times /second or 300 s-1. We measure frequency in Hertz [Hz]. So, instead we would say that the guitar string has a frequency of 300Hz.

Period Period is the time it takes for an event to complete one cycle (usually represented by T). Example: The time it takes for one complete vibration of the string would be 1/300th of a second or 1 second. 300 As you can see, period and frequency are inversely related so: Period = or T = 1 Frequency f

Writing a Lab Report Lab Reports Name: Partners’ Name: Due Date:
Lab Date: Objective: (or Purpose): In your words, not just copied from the lab handout. Materials: Rewritten from lab handout. Add or delete items as needed. Procedure: “As on lab handout”. Then note any changes you made.

Data: (or Observations): Data should be in a table with lines and appropriate units. Make sure all data is taken with the same precision. *don’t forget your uncertainty Observations must be in full sentences. Graphs: Should be on one WHOLE sheet of graph paper Should have the correct units Line of best fit (for linear data) Title/labels Correct labeling of data points USE A RULER

Questions: All questions should be answered in full sentences
Questions: All questions should be answered in full sentences. Always give your reasoning or an explanation. Conclusion: Give 3 or 4 full sentences that respond to the objective of the lab and summarize your work. You should include 2 or 3 sources of error.

Staple all rough work, especially your original data collection to your lab
YOUR LAB SHOULD BE NEAT. NEAT I SAY!

An aside…. Galileo’s thought experiment on objects at the same speed:
Two objects fall at the same speed. If you tie them together (doubling the mass) they should fall at a faster speed. They don’t. falling

Experimental Design He used experimental design. He used controlled experiments and observed objects falling from the same height. Because air resistance was always a factor he used balls rolling down an incline. The steeper the incline, the closer the model represented free fall.

His theories were used to predict the motion of many things in free fall such as raindrops or boulders.