Scientific Methods

SI Units The base units we will use in this course:

Metric Prefixes Metric Prefixes are used on SI Units to make it easier to describe the values. Prefix: Symbol: Magnitude: Meaning (multiply by): Giga- G 109 1 000 000 000 Mega- M 106 1 000 000 kilo- k 103 1000 Base 100 1 centi- c 10-2 0.01 milli- m 10-3 0.001 micro- u (mu) 10-6 0.000 001 nano- n 10-9 0.000 000 001

Unit Conversions To convert between units we use a fun little process called Dimensional Analysis. All you need is a conversion factor to multiply your number by. Example: Let’s say I want to convert 5,000 seconds into minutes, because having so many seconds laying around is impractical… First I need a conversion factor… 1 min = 60 secs And then I multiply by my conversion factor (remember you can flip the factor to cancel the units!) So: 5,000 s x (1 min / 60 s) = 83.3 minutes

Measurement When we make measurements, each measurement only has a certain degree of certainty. Measurements can only be made to a certain decimal place. The last decimal place is always an approximation. This is why we need to use Significant Figures.

Significant Figures Using ‘Sig Figs’ will let you know how precise a number is. Here are the rules: The following are all Significant figures ALL non-zero numbers (1-9) ALL zero’s between non-zero numbers (302) ALL zeros after a number that is to the right of a decimal point (0.000200) (also 2.0) ALL zeros which are to the left of a written decimal point (100. yes & 100 no) Remember, exact numbers have an unlimited number of Sig Figs. Example: one dozen = 12

How many Significant Figures? 23,450 6,345.8 0.034 0.0005670 567.00 90.01 100 4 5 2 1

Scientific Notation When we are dealing with really BIG or really small numbers, sometimes we need to describe them using scientific notation. Example: 6.022x1023 Just remember that the exponent on the 10 tells you how many places the decimal is moved to the right or left. Positive exponent->Right Negative exponent->Left There will only be one integer to the left of the decimal point.

Scientific Notation Write in scientific notation: 1,900,000 456,700,000 0.0000230 0.00000003009 1.9x106 4.567x108 2.3x10-5 3.009x10-8

Which equals 1.257×10−6 1,257,000 .000001257 .0000001257 125,700 [Default] [MC Any] [MC All]

Literal Equations We will be using a lot of Algebra in Physics… which is good because you’ve had 2 years of it, right? And you will see plenty of fun equations like these: Whenever we are working problems with equations we will need to solve for the variable we are looking for before we substitute numbers!

Literal Equations Solve this equation for G. Our goal is to get G by itself on one side of the = sign. Remember the golden rule of algebra: you have to do the same thing to both sides in order to cancel units! This means if you multiply by a variable on one side you have to multiply it on the other side!

Literal Equations (r2) (r2) (m1m2) (m1m2) Solve this equation for G. First, multiply each side by r2 to move it over to the left. Divide by (m1m2) to get rid of both variables Flip it so that G is by itself on the left side. Wasn’t that easy? (r2) (m1m2) (m1m2)

𝑇 𝑠 =2𝜋 𝑚 𝑘 , solve for m 𝑚= 𝑘 𝑇 𝑠 2 2𝜋 𝑚= 𝑘 𝑇 𝑠 2𝜋 𝑚= 𝑘 𝑇 𝑠 2 4 𝜋 2 𝑚= 𝑘 𝑇 𝑠 2 2𝜋 𝑚= 𝑘 𝑇 𝑠 2𝜋 𝑚= 𝑘 𝑇 𝑠 2 4 𝜋 2 𝑚= 𝑘 𝑇 𝑠 4 𝜋 2 [Default] [MC Any] [MC All]

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Convert 10. m/s to m/hr. 36,000 m/hr 600 m/hr .17 m/hr .028 m/hr [Default] [MC Any] [MC All]

Convert 10. m/s to km/hr. 2.8 km/hr 3.6 km/hr 28 km/hr 36 km/hr [Default] [MC Any] [MC All]

Remember: This should all be a REVIEW! Graphs Remember: This should all be a REVIEW!

Graph Basics Graphs have 2 axes: the horizontal (usually called ‘x’) and the vertical (usually called ‘y’) Graphs will be named according to what is plotted (it goes by the general form “Y” vs. “X” Each axis should always be labeled and include the proper units.

Graph Basics Lines The general equation for a line is: y = mx + b (where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept) Slope The equation for slope is

Slope What is the slope of the line in the graph? Slope (m) = (∆y / ∆x) m = (y2 – y1) / (x2 – x1) First, select two points that are far apart Plug values into the equation: m = (30 – 10) / (14 – 4) m = 2 So, the slope is 2, but what are the units, and what do they mean? In this case, the units would be (smiley faces / puppies) or /p And this tells us that you would get 2 smiley faces for every puppy you see!

Graphs What is the y-intercept of the graph and what does that mean? The y-intercept is 2 and it means that even with 0 puppies you can have a happiness of 2 What is the mathematical representation (equation) for our graph? y = mx + b y = 2x + 2 or H = 2P + 2

Identify the graph. 𝑦=2(𝑥− 3 2 ) 𝑦=2(𝑥+ 3 2 ) 𝑦= 1 2 (𝑥−6) 𝑦= 1 2 (𝑥+6) [Default] [MC Any] [MC All]

Proportional Reasoning Identifying relationships between variables is crucial in physics. Two variables are said to be directly proportional when they are each affected in the same way as the other when multiplied by a constant. For instance, in the equation y = kx , y and x are directly proportional because if you were to double y, x would have to double as well. Two variables are said to be indirectly proportional when one variable is affected inversely when the other is multiplied by a constant. For instance, in the equation y = 1/x , y and x are indirectly proportional because if you were to double x, y would be halved.

Proportional Reasoning Two variables are said to be directly related when one variable increasing causes the other to increase as well. Two variables are indirectly (inversely) related when one variable increasing causes the other to decrease.

Linearization Occasionally, you might run into a graph that is not linear, like the one below. This presents a problem, because we cannot do much of an analysis with a curved line. This means we need to linearize the graph (turn it into a straight line)

Linearization First, you need the equation for the line. For this one, it is conveniently y = x2, or p = t2 To linearize the data and obtain a straight line, we will need to plot a Position vs. Time2 graph instead.

The Scientific Method The scientific method comes in many different forms but always has these basic steps: Ask a question Develop a hypothesis (An if/then statement describing what you think will answer the question) Design an experiment Analyze data and draw conclusions

The Scientific Method Let’s do a real world example: Timmy is a geek and is having a hard time making friends… He just wants to be friends with the cool kids…

The Scientific Method So Timmy decided to use the scientific method: First he asks his question: “How can I be a cool kid?” Then he develops a hypothesis – an if/then statement that should answer his question or solve his problem. “If I take showers every day, then I can be friends with the cool kids!” He designs an experiment: “I’ll take a shower every day and record how many words the cool kids say to me each day.” He performs his experiment for a certain amount of time and records all his data.

The Scientific Method So Timmy decided to use the scientific method: He analyzes his data and draws conclusions: He made a graph to display his results: There is a direct relationship between how many days he showers and how much the cool kids talk to him!

The Scientific Method Now he can draw a conclusion based on his data: Timmy concluded that he is now cool and is friends with the other cool kids!

Experimental Variables In any experiment, it is important to identify the variables that are being affected or kept the same. There are three types: The Independent Variable This is the what you change to see what will happen. Example: For Timmy this was how many days in a row he took a shower. The Dependent Variable This is what you hope is affected by the Independent Variable. Example: How many words a day the cool kids say to Timmy. Constants This is everything that was not a part of the experiment but needed to be kept constant. Example: even though Timmy showered, he still never put on deodorant or stopped playing video games for 12 hours a day. Those variables were held constant.

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