Metrics and Conversions

Physics Fall 2014

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 1Liter or with 20 oz?

Mathematics is the Language of Physics (and science in general)

Some dimensions we will measure are:1. Mass2. Volume3. distance4. Time5. Temperature Write their definitions and the units of

measure we should use.

You also want to know what dimension or aspect of an item or phenomenon you are measuring

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.

Some measurements are more complex

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.

Sometimes…

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

First: Multiplying fractions review

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?

Cancel out if possible

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

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 roses1 pair shoes 1 dozen roses

Conversions cont’d

◦ fractions in which the value of the numerator is equal to the denominator, but the units , and therefore also the numbers, are different.

Conversion Factor

Can you think of any you might already use?

Use a conversion factor to convert 3 hours into minutes:

1. What is the conversion factor? There are 60 minutes in an hour so: 1hr or 60 min

60 min I hr

2. Set up the problem3 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:

Convert this:

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 does this have to do with science?

◦ Used for different scientific measurements◦ Based on the number “10”◦ Base units depend on the dimension or aspect

you are measuring for example:

dimension unit Mass gram Volume liter Distance (length) meter

What do you remember/know about metrics?

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

Metric terms

Note: the prefix is not a unit of measure, so it cannot stand alone.

To help you remember the prefixes in order: Killer Hippos Digging Under Dirt Can’t March

Or you may already knowKing Henry Died by Drinking Chocolate Milk

Mnemonic

For example: Kilometer vs. Millimeter Kiloliter vs. Milliliter Decaliter vs. Centiliter

The prefix is used with a base unit of measure to represent a larger or smaller unit of the same type of dimension.

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

Conversion factors for metrics

◦ Conversion factors examples:1 Km or m 1000 mm or m1000m Km 1 m cm

cm or m m cm

dimensional analysis

Convert 3.5 m to cm1. What is the correct conversion factor? 1m or 100 cm100 cm 1m2. Solve the problem 3.5 m x 100 cm = ________ cm 1 1 m

Let’s convert!

** Which conversion factor will allow you to correctly cancel your starting units and leave you with the correct ending units? **

Covert 2.56 mm to m1. What is the correct conversion factor?

2. Set up the problem and solve

We’ll work one together

Convert 3.4 Km to m

Your turn!

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 1000m 1 Km2. 1 m or 100 cm 100 cm 1 m

So we will use 1000 m and 100 cm 1Km 1m

A bit more difficult

** Which conversion factor will allow you to correctly cancel your starting units and leave you with the correct ending units? **

Solve the problem:

1.25 Km x 1000 m x 100 cm = 1 1 Km I m

Note you will cancel out both units in the first conversion factor

Now you have to line them up

Covert 3.2 mm to Hm1. What is the correct conversion factor?

2. Set up the problem and solve

Work it together

Convert 93.2 cm to Dm

On your own

Complete the conversion worksheet that will be passed out

Homework:

So let’s make it a bit harder◦ Can you convert 8km/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

8Km x m x hr x min = m/s 1 hr Km min s

This is too easy….

Convert 575 Km/hr to cm/min

575Km x x x = cm/min 1 hr

Let’s do another one together

Convert 2500 cm/sec m/min

One more for good measure