Upload
aniyah-brittin
View
215
Download
1
Tags:
Embed Size (px)
Citation preview
SPH3UIB DAY 3/4/5 NOTES
METRIC SYSTEM,GRAPHING RULES, LOG-LOG DATA ANALYSIS
Metric System
Metric prefix word
Metric prefix symbol
Power of ten
nano n 10-9
micro µ 10-6
milli m 10-3
centi c 10-2
kilo k 103
mega M 106
giga G 109
Metric system
The standard units in Physics are kilograms (kg), seconds (s) and metres (m).
The Newton (N) is 1 kgm/s2 and The Joule (J) is 1 kgm2/s2.To use standard units, students must be able
to convert units to standard units for effective communication of data in labs.
Examples12.0 cm is converted into metres by shifting the
decimal place left two spaces. 12.0 cm = 0.120 m12.0 g is converted into kg by dividing by 1000 or
shifting the decimal left three times. 12.0 g = 0.0120 kgIf 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 = 0.0000120 kg = 1.20 x 10-5 kg.
Metric practice
Convert to standard units: kg, m, s:
1) 12.0 µm
2) 33.45 mm
3) 12.0 µg
4) 12.67 ns
5) 123.4 Gm
6) 7654 Mg
7) 45.258 Ms
8) 0.000458 km
9) 0.025478 cs
Metric practice
Convert to standard units: kg, m, s:
1) 12.0 µm 1.20 x 10-5 m
2) 33.45 mm 0.03345 m
3) 12.0 µg 1.20 x 10-8 kg
4) 12.67 ns 1.267 x 10-8 s
5) 123.4 Gm 1.234 x 1011 m
6) 7654 Mg 7.654 x 106 kg
7) 45.258 Ms 4.5258 x 107 s
8) 0.000458 km 0.458 m
9) 0.025478 cs 2.5478 x 10-4 s
Graphing ExpectationsUse 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 of y vs. x
(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 ExpectationsA best fit line or curve is usually expected for
all graphs.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 relationshipsOnce 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 motiond t
time (s)
distance (m)
1 282 563 844 1125 140
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)
5 0.2
10 0.1
20 0.05
50 0.02
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 v2. If the speed triples, how many times greater is the force?
F = kv2 means thatF1 = k v1
2 and a new force F2 = k v22.
Taking a ratio of these two expressions eliminates the “k” constant.F
F
v
v1
2
12
22
Example 1 – algebraic solution
F
F1
2
1
9
F
F
v
v1
2
12
22
F
F
v
v
1
2
12
1
23
F2 = 9F1
Ratios and Proportions ws
Answers are on the bottom of the page
Log-Log Data AnalysisOne method is to re-plot data by changing the
manipulated (x-axis) data to see its effects on the responding (y-axis) variable.
This can be tedious and prone to human error.Using the rules of logarithms, a quicker and
more efficient method arises to find an equation.
Any curved graph can be expressed as:
y = kxn
Log-Log Data Analysisy = kxn
Taking the log of both sides and using log rules:
log y = logkxn
log y = log k + nlog x
log y = nlog x + log kThis is now in a form like y = mx + b, where the
slope is “n”, the exponent of the relationship. The y-intercept will also give the value for k (log k,
which can be converted to k), which is the constant (but if axes are broken, a re-plot will yield “k”).
Log-Log Data AnalysisStep 1: Take the log of all data and plot these
numbers as log y versus log x. (log d vs. log t)Step 2: Find the slope. The slope of this graph
yields “n” and has no units. (n uses s.d. from data)Step 3: Re-plot the graph as y versus xn, which will
yield a straight line verifying your value of “n”.Step 4: Find the slope. The slope of the second
graph yields the value, with units, of “k”.Step 5: The final equation can be stated in its final
form as y = kxn.
Log Log Assignment
Do practice first, then assignment due Friday.