Metrics and Conversions Physics Fall 2014 Mathematics is

Metrics and Conversions Physics Fall 2014

Mathematics is the Language of Physics (and science in general) � One of the simplest applications of math in physics is to measure things. � The key to communicating measurements is to remember the number cannot be naked – the number needs to be followed by the units it represents. � You want to use units of measure that are standardized. � Would you be getting more soda with 1 Liter or with 20 oz?

You also want to know what dimension or aspect of an item or phenomenon you are measuring � Some dimensions we will measure are: 1. Mass 2. Volume 3. distance 4. Time 5. Temperature � Write their definitions and the units of measure we should use.

Some measurements are more complex � For example: � Speed and acceleration � They involve rates or comparisons of two unlike dimensions � Speed = distance compared to time � We will define and write units for these very soon.

Sometimes… � You have to measure with equipment that does not allow you to measure in the standard measurement units for a particular physics dimension such as with speed. �Let’s look at how to approach this issue.

First: Multiplying fractions review � When given a problem like this: 1 x 2 = __ 5 3 how do you solve it? � You multiply straight across! � Do this one on your notes: 3 x 3 = __ 2 4

Cancel out if possible � What about if you are given this problem: 3 x 2 = __ 4 3 � You could multiply straight across and then simplify… � or you could cancel out first to make the problem easier So, where are we going with these math skills?

Conversions � what does it means to convert? ◦ To convert means to change from one to another ◦ But at this time what are we converting between? �Usually in science it is from one unit to another �In a scientific measurement answer : A unit is a word or abbreviation that comes after the number and describes what that number means. �And again, why is important to include units with numbers 100 Vs 100 dollars vs 100 cents vs 100 miles

Conversions cont’d � How many shoes do you have if you have 6 pairs of shoes? ◦ How did you figure out that you would have 12 shoes? � How many roses do you have if you are given 4 dozen roses? ◦ How did you figure out that there would be 48 roses? � The fact that there are 2 shoes in a pair of shoes or 12 roses in a dozen roses represent a 2 shoes 12 roses 1 pair shoes 1 dozen roses

Conversion Factor ◦ fractions in which the value of the numerator is equal to the denominator, but the units , and therefore also the numbers, are different. Can you think of any you might already use?

Convert this � Use a conversion factor to convert 3 hours into minutes: 1. What is the conversion factor? �There are 60 minutes in an hour so: 1 hr or 60 min I hr 2. Set up the problem 3 hr x ______ = ______ min 1 *** remember, you want to cancel hours and be left with minutes, so which of the two versions of this conversion factor will you use?

Convert this: � Use a conversion factor to convert 360 minutes into hours: 1. What is the conversion factor? 2. Set up the problem

Convert this: � Use a conversion factor to convert 96 inches into feet:

What does this have to do with science? � Only the method used to convert values of measurements that are equal. � In the US, we use a group (or system) of measurement units called the empirical system. � In science we use METRICS!!!!

What do you remember/know about metrics? ◦ Used for different scientific measurements ◦ Based on the number “ 10” ◦ Base units depend on the dimension or aspect you are measuring for example: dimension �Mass �Volume �Distance (length) unit gram liter meter

Metric terms � Prefixes are parts of words that come “before” another word or word part � Metric ◦ ◦ ◦ ◦ prefixes: Kilo (K) = 1000 Hecto (H) = 100 Deca (D) = 10 Base unit = 1 deci (d) = 1/10 centi (c) = 1/100 milli (m) = 1/1000 Note: the prefix is not a unit of measure, so it cannot stand alone.

Mnemonic � To help you remember the prefixes in order: � Killer Hippos Digging Under Dirt Can’t March � Or you may already know King Henry Died by Drinking Chocolate Milk

The prefix is used with a base unit of measure to represent a larger or smaller unit of the same type of dimension. � For example: � Kilometer vs. Millimeter � Kiloliter vs. Milliliter � Decaliter vs. Centiliter

Conversion factors for metrics �Up to this point, you have probably converted between the metric prefixes by simply moving the decimal, right? ◦ Not anymore! ◦ Now, you must use/show the correct conversion factors when converting between the various prefixes – this is called dimensional analysis

dimensional analysis ◦ Conversion factors examples: 1 Km or 1000 m cm or m m Km m cm 1000 mm or 1 m m cm

Let’s convert! � Convert 3. 5 m to cm 1. What is the correct conversion factor? ** Which conversion factor will 1 m or 100 cm allow you to correctly cancel your 100 cm 1 m starting units and leave you with the correct ending units? ** 2. Solve the problem 3. 5 m x 100 cm = ____ cm 1 1 m

We’ll work one together � Covert 2. 56 mm to m 1. What is the correct conversion factor? 2. Set up the problem and solve

Your turn! � Convert 3. 4 Km to m

A bit more difficult � Convert 1. 25 Km to cm � Can you go directly from Km to cm? ◦ No, you have to do this in two steps so you need two conversion factors 1. 1 Km or 1000 m 1000 m 1 Km 2. 1 m or 100 cm 1 m So we will use 1000 m 1 Km ** Which conversion factor will allow you to correctly cancel your starting units and leave you with the correct ending units? ** and 100 cm 1 m

Now you have to line them up � Solve the problem: 1. 25 Km x 1000 m x 100 cm = 1 1 Km Im v Note you will cancel out both units in the first conversion factor

Work it together � Covert 3. 2 mm to Hm 1. What is the correct conversion factor? 2. Set up the problem and solve

On your own � Convert 93. 2 cm to Dm

Homework: � Complete the conversion worksheet that will be passed out

This is too easy…. � So let’s make it a bit harder ◦ Can you convert 8 km/hr into m/s? ◦ Of course you can – this is called a double conversion �Where you are converting two different units in the same problem �The key to solving these is to convert them separately 8 Km x 1 hr mx Km hr x min = s m/s

Let’s do another one together � Convert 575 Km x 1 hr 575 Km/hr to cm/min x x = cm/min

One more for good measure � Convert 2500 cm/sec m/min