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 The base units we will use in this course: Metric Prefixes are used on SI Units to make it easier to describe the values. Prefix:Symbol:Magnitude:Meaning.

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Presentation on theme: " The base units we will use in this course: Metric Prefixes are used on SI Units to make it easier to describe the values. Prefix:Symbol:Magnitude:Meaning."— Presentation transcript:

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2  The base units we will use in this course:

3 Metric Prefixes are used on SI Units to make it easier to describe the values. Prefix:Symbol:Magnitude:Meaning (multiply by): Giga-G10 9 1 000 000 000 Mega-M10 6 1 000 000 kilo-k10 3 1000 Base10 0 1 centi-c10 -2 0.01 milli-m10 -3 0.001 micro-u (mu)10 -6 0.000 001 nano-n10 -9 0.000 000 001

4  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

5  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.

6  Using ‘Sig Figs’ will let you know how precise a number is.  Here are the rules: The following are all Significant figures 1.ALL non-zero numbers (1-9) 2.ALL zero’s between non-zero numbers (302) 3.ALL zeros after a number that is to the right of a decimal point (0.000200) (also 2.0) 4.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

7 1. 23,450 2. 6,345.8 3. 0.034 4. 0.0005670 5. 567.00 6. 90.01 7. 1004524541

8  When we are dealing with really BIG or really small numbers, sometimes we need to describe them using scientific notation.  Example: 6.022x10 23  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.

9 Write in scientific notation: 1. 1,900,000 2. 456,700,000 3. 0.0000230 4. 0.00000003009 1.9x10 6 4.567x10 8 2.3x10 -5 3.009x10 -8

10 A. 1,257,000 B..000001257 C..0000001257 D. 125,700

11  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!

12  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!

13  Solve this equation for G.  First, multiply each side by r 2 to move it over to the left.  Divide by (m 1 m 2 ) to get rid of both variables  Flip it so that G is by itself on the left side.  Wasn’t that easy? (r 2 ) (m 1 m 2 )

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16 A. 36,000 m/hr B. 600 m/hr C..17 m/hr D..028 m/hr

17 A. 2.8 km/hr B. 3.6 km/hr C. 28 km/hr D. 36 km/hr

18 Remember: This should all be a REVIEW!

19  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.

20  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

21  What is the slope of the line in the graph?  Slope (m) = (∆y / ∆x) m = (y 2 – y 1 ) / (x 2 – x 1 )  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!

22  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

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24  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.

25  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.

26  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)

27  First, you need the equation for the line. For this one, it is conveniently y = x 2, or p = t 2  To linearize the data and obtain a straight line, we will need to plot a Position vs. Time 2 graph instead.

28  The scientific method comes in many different forms but always has these basic steps: 1. Ask a question 2. Develop a hypothesis (An if/then statement describing what you think will answer the question) 3. Design an experiment 4. Analyze data and draw conclusions

29  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…

30  So Timmy decided to use the scientific method: 1. First he asks his question: “How can I be a cool kid?” 2. 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!” 3. He designs an experiment: “I’ll take a shower every day and record how many words the cool kids say to me each day.” 4. He performs his experiment for a certain amount of time and records all his data.

31  So Timmy decided to use the scientific method: 4. 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!

32  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!

33  In any experiment, it is important to identify the variables that are being affected or kept the same. There are three types: 1. 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. 2. 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. 3. 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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