SPH3UIB DAY 3/4 NOTES METRIC SYSTEM,GRAPHING RULES

Metric System Metric prefix word Metric prefix symbol Power of ten nanon10 -9 microµ10 -6 millim10 -3 centic10 -2 kilok10 3 megaM10 6 gigaG10 9

Metric system  The standard units in Physics are kilograms (kg), seconds (s) and metres (m).  The Newton (N) is 1 kgm/s 2 and  The Joule (J) is 1 kgm 2 /s 2.  To use standard units, students must be able to convert units to standard units for effective communication of data in labs.

Examples  12.0 cm is converted into metres by shifting the decimal place left two spaces.  12.0 cm = m  12.0 g is converted into kg by dividing by 1000 or shifting the decimal left three times.  12.0 g = kg  If a mass is given as 12.0 mg, then the decimal shifts left 3 times to grams and then 3 more to kg. Once we get to really small/large numbers, scientific notation is needed.  12.0 mg = kg = 1.20 x kg.

Metric practice  Convert to standard units: kg, m, s: 1) 12.0 µm 2) mm 3) 12.0 µg 4) ns 5) Gm 6) 7654 Mg 7) Ms 8) km 9) cs

Metric practice  Convert to standard units: kg, m, s: 1) 12.0 µm  1.20 x m 2) mm  m 3) 12.0 µg  1.20 x kg 4) ns  x s 5) Gm  x m 6) 7654 Mg  x 10 6 kg 7) Ms  x 10 7 s 8) km  m 9) cs  x s

Graphing Expectations  Use a full page of graph paper for graphs in lab reports or assignments.  Include the variable and units on each axis (distance (m), time (s), etc.)  The title of the graph is in the form y vs. x (Ex: distance versus time, no units needed in title).  Calculations are NOT done on the graph, but on a separate page.  Errors are indicated by circling dots if no absolute error is known, or error bars for labs.

Graphing Expectations  A best fit line or curve is usually expected for all graphs. (Note: a curve can be a best fit line!)  Slope calculations: include units and are rounded based on sig digs (determined by precision of measuring devices in the lab (absolute error)).  Use +/- half the smallest division of measuring devices in labs, for precision and to determine how many decimals you must measure to.

Graph data from error worksheet  Plot displacement versus time and velocity versus time.

Determining data relationships  Once data is plotted, several general shapes may arise: linear, power or inverse (possibly a root curve).  If a curve results, we wish to determine the relationship between the variables.  Once we get a linear graph, we can determine an equation for the data (and a formula may ensue).

Ratios and Proportions  The statement of how one quantity varies in relation to another is called a proportionality expression.  The goal in physics is to correlate observational data and determine the relationship between the two variables: dependent and independent.  We need to take data and determine a relationship and find how the change in one quantity affects the other.

Example 1 Notice that as time doubles, so does distance. As time triples, distance triples. This is a direct relationship (or direct variation). This object is undergoing uniform motion d  t time (s) distance (m)

Example 2 Notice that as frequency goes from 5 to 50, (a factor of 10), the period changed from 0.2 to 0.02 (a factor of 1/10). ƒ  1/T Frequency (Hz) Period (s)

Ratios and Proportions  Any proportionality can be expressed as an equation by adding a proportionality constant (use the letter “k”, typically).  From Ex. 2: ƒ = k (1/T)  The “k” constant can be calculated with known values. (We could take numbers from Example #2 and sub in all the values and find the average “k” value.)

Ratios and Proportions Chart ws  Chart 1 will be done as an example in class.

Example 1 – algebraic solution  You are given that F  v 2. If the speed triples, how many times greater is the force?  F = kv 2 means that  F 1 = k v 1 2 and a new force F 2 = k v 2 2.  Taking a ratio of these two expressions eliminates the “k” constant.

Example 1 – algebraic solution F 2 = 9F 1

Example 2 – algebraic solution Given Force is inversely proportional to distance squared, find the new force if the distance is quartered.

Ratios and Proportions ws  Answers are on the bottom of the page