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## Introduction to Physics

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**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.**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 (SystèmeInternational)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 – 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.**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 = 1 and 106 m = 1 106 m 1Mm • 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. 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. 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, 3.000 are of the same value, but 3.000 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. 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. 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 (0.0005 has only one sig. fig.) 2. tailing zeroes in numbers withoutdecimal pointsare ambiguous. (zeroes in 700 are not, but the zeroes in 700.0 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 5.200 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.)**0.0050200 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 5.35 658.05 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:**(10.2 + 2.45) 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:**(32.01 + 12.2) x 623 = 44.21X623 =27542.83 =2.75X104**Example 4**=(.02 +.612) x 3.12 =(.02 + .3721) x 3.12 =(.3921) x 3.12 =1.223352 =1.2**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.**Independentvariables 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”