Measurements&

Mathematics

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A Review of Necessary Math Skills

In this course, we frequently use ______________, _______________, and ___________________.

AlgebraOften, we will have to _________________ an equation to solve for an unknown variable.

Example 1 : Solve for x in the following equation: 8=4 x .

Steps:

Example 2 : Solve for c in the following equation: a=bc

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Classwork Practice

1) Given d= ef , solve for e.

2) Given the same equation as #1, solve for f.

3) Given g=hi+j, solve for i.

4) Given V=IR, solve for R.

5) Given P=Wt , solve for t.

6) Given a= Fm, solve for F.

7) Given v f=v i+at, solve for a.

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8) Given k=12m, solve for m.

9) Given n=p2, solve for p

Measurements & MathematicsPhysics is based on observations and measurements of the physical world.

Consequently, scientists have developed tools for measurement and adopted standard conventions for describing natural phenomena. These conventions are reviewed below.

Units

Unit –________________________________________________________________________________________________________________________________

Ex – Without Units With Units

The SI System - ______________________________________________________________________________________________________________

o All quantities measured by physicists can be expressed in terms of seven fundamental units.

Fundamental Units

Kind of UnitQuantity Being

Measured Name of UnitSymb

olFundamental SI

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Derived Units – _____________________________________________________________________

_____________________________________________________________________ Ex –

Scientific NotationMeasurements that have very large or very small values are usually expressed in

scientific notation.

Scientific Notation - ________________________________________________________________

________________________________________________________________ ________________________________________________________________

Calculating with Scientific Notation To input 2.56 x 105 into your calculator, type

_______________________________________

If you get an answer that looks like , report ______________________________

The Balancing ActConvert the following values into proper scientific notation.

167400000 m

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Order of Magnitude EstimationsIn many cases, it is not necessary or even feasible to calculate the exact solution to a physics problem. Instead, one can attempt an "Order of Magnitude Estimate" to get a rough idea of the answer. This is especially useful during experiments - where, although you don't know the exact result, a rough calculation can give you an idea of what the result will be - so you can look for it effectively.

_______ 0.01 _______ 1 _______ 100 _______ 10,00010-3 _______ 10-1 _______ 101 _______ 103 _______

Estimate each of the following quantities to the nearest order of magnitude (power of ten).

For example: Estimate the number of students in this room to the nearest order of magnitude. Suppose there are 24 students in class. 24 is closer to 101 than it is to 102 or 100.

Answer: 101 students

1. The number of students enrolled at POBJFKHS

2. The number of teachers at POBJFKHS

3. The number of seconds in this physics period

123 x 102 s

.005 x 10-9 kg

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4. The mass of a nickel in grams (Hint: A few paperclips have a massof one gram.)

5. The height of the door in meters

6. The width of the door in meters

7. The thickness of the door in meters

8. The mass of a couch in pounds

SI PrefixesWhat could you do if measuring in meters were inconvenient because the distance you were measuring was too big or too small?

Prefix - _____________________________________________________________________________

_____________________________________________________________________________ _____________________________________________________________________________

Prefix Symbol Notation

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p. 1 on Reference Tables

? ? ? ? ? ? ? ? ? ? ? ? Questions ? ? ? ? ? ? ? ? ? ? ?

1. The energy in half a tank of gasoline is 1,000,000,000 joules. Express this value in gigajoules.

2. The mean radius of Earth is 6,000,000 meters. Express this value in kilometers.

3. Convert 700 picoseconds into seconds.

4. Human hair grows at a rate of 3 nanometers per second. Express this rate in meters per second.

Converting UnitsDue to such a variety in units (non-SI, SI, and English), conversions are often necessary.

Ex - 1 day = 24 hours (hr)

1 foot (ft) = inches (in) 1 hour (h) = minutes (min)1 inch (in) = centimeters (cm) 1 minute (min) = seconds (s)1 meter (m) = yards (yd) 1 kilogram (kg) = pounds (lb)1 mile (mi) = kilometers (km) 1 yard (yd) = feet (ft)

1. Convert 4.5 hours (h) into seconds (s).

2. Your friend weighs 125 pounds (lbs). Convert this value to kilograms (kg).

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3. If you run a 10. K (kilometer) race, how many miles (mi) did you run?

Using the conversion table on your Reference Table, complete the following conversions.

4. Convert 5 electronvolts(eV) into Joules (J).

5. Convert 2.00 Coulombs (C) into elementary charges (e).

Tools for MeasurementsElectronic – a device that has a _______________________________________of the measurement

Record the __________________________________________________, ________________ ________________ the value.

Mechanical – a device that is __________________________________________________________ that the ________________________________________________________________

Record value to the ______________________________________________ based upon the ____________________________________________________

For example:

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o If measuring something _________________, record to the nearest _____________.

o If measuring something _____________________________________, record to the nearest _____________.

Measuring LengthTools Units Technique

← ______________cm

← ______________m

← ______________cm

← ______________m

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Measuring MassTools Units Technique

← ____________ g

← ____________ kg

____________ g →

____________ kg →

← ____________ g

← ____________ kg

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____________ g →

____________ kg →

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Measuring TimeTools Units Technique

← ____________ s

____________ s →

Measuring Force (Weight)Tools Units

____________ N →

Measuring AngleTools Units Technique

Angle from the horizontal:

__________________ 0

Angle from the vertical:

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__________________ 0

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Data Analysis Percent Error – a measure of how inaccurate a measurement or value is

when compared to the actual value.

Mean Value – the arithmetic average is a measure of the “middle” value of the data set

o The average value of all of the measurements taken

Significant FiguresSignificant figure (digit) – the digits that are

______________________________________________ plus one digit whose value has been _______________________________________ in a _______________________________ value

The ________________________ the number of significant figures in a measurement, the _____________________ the _________________________ of the measurement.

Rules for Significant Figures

Rule #1Nonzero digits in a measurement are always significant.

Rule #2Zeros that appear before a nonzero digit are NOT significant.

Ex –

Rule #3Zeros that appear between nonzero digits are significant.

Ex –

Rule #4Zeros that appear after a nonzero digit are significant only if:

(a) followed by a decimal point

* Not on Reference Table

* Not on Reference Table

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Ex – (b) they appear to the right of the decimal point.

Ex –

Types of GraphsLinear Relationships

Graph Shape Relationship General Equation

Non-Linear Relationships

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Graphing Conventions

1. Let your graph take up most of the page.

2. Determine the independent variable. This is located on the x-axis.

3. Determine the dependent variable. This is located on the y-axis.

4. Label each axis with variable and unit.

5. Choose an appropriate range for each axis. Use appropriate spacing between numbers.

6. Title your graph. (Dependent vs. Independent)

7. Circle each data point for visibility.

8. Draw your best-fit line or curve. Never (almost) play connect-the-dots.

9. If the best fit line is straight, calculate the slope of the line using

Use two points ON the line (these may or may not be data points).

Put a box around each point used and state their coordinates

* Not on Reference Table

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Show your calculations, including formula and substitutions. Express the result as a decimal and show units!

10. Determine the physics formula associated with your graph using the slope equation.

11. Consider the physical significance of the slope. Does it have a meaning or a specific name?

12. Express the slope of your graph as a physical value.

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Graphing DataThe position of a moving car was measured at one-second intervals and recorded in the following table. Graph the data on the grid provided and draw the line of best fit. Determine the slope of the line.

Time (s) Position (m)

0.0 01.0 172.0 383.0 644.0 795.0 102

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