Metric System TEN. Deci-.1. Deka- Basic Unit. Kilo= Centi= Milli= The Meter is the basic unit of length in the SI (SI = International System)

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1 Metric System TEN All units are based on the power of! Basic Unit Kilo- Hecto- Deka- Deci-.1 Centi-.01 Milli-.001 Bold boxes are prefixes you MUST know! or 1/ or 1/1000 Kilo= Centi= Milli= The Meter is the basic unit of length in the SI (SI = International System) There are meters in a kilometer There are centimeters in a meter. 3. There are millimeters in a meter. The Gram is the basic unit of mass in the SI system (SI = International System) therefore, 1. There are grams in a kilogram. 2. There are milligrams in a gram. 3. There are milligrams in a kilogram Try these conversions: ,000, mg = g 1 kg = g cm = mm 14km = m Compare using <,> or = g = kg < > 56cm 6m 250m = km 7g 698 mg = = 1500mg 1.5g 536cm 5.36m 1

2 Can you name these 3 countries? US Liberia Myanmar The countries in grey use the metric system! English Units Confusing? Length Digit = 3/4 inch Furlong= The distance a plough team could be driven without rest League- Usually three miles. Intended to be an hour's walk. Volume Jigger- 2 mouthfuls Jack- 2 Jiggers Jill- 2 Jacks Cup- 2 Jills Pint- 2 Cups Quart- 2 Pints Pottle- 2 Quarts Gallon- 2 Pottles Peck- 2 Gallons Kenning- 2 Pecks Bushel- 2 kennings Cask- 2 Bushels Barrel- 2 Casks Hogshead- 2 Barrels 2

3 Colbert Report Definitions Length Width Height Measurement Unit -Length and Area Notes- Diameter- Length of a circle through its midpoint. Diameter Radius- Half the diameter Radius 3

4 Common units used in science - Metric System Unit Millimeter Centimeter Meter Kilometer Abbreviation mm cm m km Equivalent ~1/16th inch ~ 1/2 inch ~ 1 yard (3 ft.) ~.6 mi Usually we use mm until it s 1cm long, then we use cm until it s 1m long and m until it s 1 km long. How to measure: 1. Line up the end of the object with the ruler. 2. Count the total number of centimeters. 3. The # of millimeters last the last cm is the decimal. Formulas we commonly use (memorize): Area of a rectangle: A = Length x Width Area of a circle: Circumference: A = Πr 2 C=Πd When asked to show work you are required to do the following: 1. Write the formula used. 2. Plug the numbers into the formula. 3. Calculate and write the answer. 4. Put units on your answer. 4

5 Examples:.4cm 5cm 3.6cm 1. A= L ( W) 2. A= 3.6cm x.4cm 3. A= 1.44cm 2 1. A= (L)(W) 2. A= 5cm x 5cm 3. A= 25cm 2 Examples: Find the circumference and area of the circle Circumference Area 1. C= Πd 1. A= Πr 2 Diameter = 5cm 2. C= (3.14)5cm 3. C= 15.7cm 2. A= (3.14)(2.5cm) 2 3. A= cm 2 Volume How to Measure Volume Solids There are 2 methods: 1. If it is a regular shaped object you can measure with a ruler and calculate the volume. (This means that there is a math formula to use) Formulas: Amount of space something takes up Volume Box Volume of a cylinder 1cm 2cm 6cm 8cm V=Πr 2 h 3cm V=lwh V=(3cm)(1cm)(2cm) V=6cm 3 V=(3.14)(3cm) 2 (8cm) V=(3.14)(9cm 2 )(8cm) V=226.08cm 3 5

6 Measuring volume of liquids 1. Pour liquid into graduated cylinder 2. The curve formed by the liquid is called the meniscus, always read the bottom meniscus 11.5ml Measuring volume of gases Gases take up as much space as you give them so they have no definite volume. The volume of a gas can change by applying more or less pressure Measuring Volume Units Milliliter (ml) Cubic Centimeter (cm 3 ) Note: 1 ml = 1 cm 3 they take up the same amount of space If it is an irregular shaped solid use the water displacement method 1. Put a quantity of water in a graduated cylinder 2. Record the volume of water 3. Add the object, record the volume of the water 4. Subtract to determine the volume of the object Example. You put 55ml of water in a graduated cylinder Your add a small rock You read the volume of water it is 63ml Subtract to determine the volume of the rock to be 8ml 6

7 Mass the amount of matter in an object The Law of conservation of matter 1. Matter cannot be created 2. Matter cannot be destroyed 3. Matter can change forms Units used for measuring mass Unit Abbreviation Equivalent Kilogram kg ~2.2 pounds Gram g ~mass of a pen cap Milligram mg ~ 1/1000 th of a gram Measuring Mass Triple Beam Balance rider beam pointer (at zero) pan zero knob Procedure: 1. Slide all riders to zero point. Make sure pointer swings freely and points to zero. 2. If it does not point to zero adjust it using the zero knob 3. Place object to be measured on the pan. Slide the riders along the beams until the pointer is at zero 4. Add up the value of each rider to calculate the total mass 7

8 Measuring Mass Digital Balance pan zero button display Procedure: 1. Press the zero button. This sets the balance to zero before you begin measuring 2. Place object on the balance 3. Read the display to determine mass 4. You can have the balance subtract the mass of a container automatically. Place the empty container on the balance. Press the zero button. Put your sample in the container. Place it back on the pan. The mass displayed is the mass of the sample. Determine how many grams would be sitting it the pan if the riders were in the position that they are below Total Mass: 175 g Total Mass: 328 g 8

9 Mass Mass vs. Weight They are NOT the same thing. Many people use the words interchangeably but they are not the same thing. Example: The amount of matter in a material is the same no matter where it is. Weight How much stuff is in an object. Does NOT change with location. Measured in grams (g). Determined by the amount of mass an object has and the force of gravity pulling on that object. Weight Formula -> Weight = Mass x Gravity units used = Gravity is dependent on: Newtons 1) Size of an object 2) The distance from the center of a planet What happens to your mass and weight at these locations? (Use >,<. Or =) Gravity on Earth Gravity on Moon Weight on Earth Weight on Moon = > > Mass on Earth Mass on Moon > Gravity on Jupiter Gravity on Earth > Weight on Jupiter Weight on Earth = Mass on Jupiter Mass on Earth 9

10 What happens to your mass and weight at these locations? (Use >,<. Or =) Mountain Top Gravity on the mountain top Gravity in the valley Weigh on the mountain top Weight in the valley < < Valley Summary: Mass Your never changes Weight Your can change Example: There force of gravity on the moon is only about 1/6 th of the force of gravity on the Earth (because the moon is much smaller than the Earth). If you go to the moon your mass is the same, you still have the same amount of matter (or stuff) in your body. But because the force of gravity is less, your weight is about 1/6 th of your weight on Earth. Force of gravity on Earth = 9.8 m/s 2 Force of gravity on Moon = 1.64 m/s 2 Weight= Mass x Force of Gravity Earth Your mass 70 kg Your weight 687 N Moon 70 kg 115 N Remember: Your mass does not change with location, your weight can 10

11 Gravity on the Moon Mass vs. Weight In the above picture Mr. Arcuri just got done winning yet another bodybuilding contest. The judges are weighing him to see if he competed in the proper weight class. Determine Mr. Arcuri s weight. (Hint: He is at sea level and on planet Earth where gravity equals 9.81 m/s 2 ) 100kg Mr. Arcuri s Mass is: Mr. Arcuri s Weight is: 981 Newtons Scale reads= 100kg Mr. Arcuri continues to compete in the intergalactic bodybuilding competition. His first competition is at Mount Olympus on Mars. The gravity on Mars is 3.75 m/s 2. Mr. Arcuri s Mass is: 100kg Mr. Arcuri s Weight is: 375 Newtons On Earth do bodybuilders / wrestlers actually compete in weight classes or mass classes? Explain. Mass classes 11

12 Hammer vs. Feather in Free Fall Density Amount of matter in a given space How compact the molecules are in a substance 1. The density of a substance at a given temperature does not change The density of a tiny speck of gold is the same as a gold coin If I have a bar of aluminum with a density of 2.7g/cm 3 and I cut it in 3 pieces, each piece still has a density of 2.7g/cm 3. Therefore I can use density to identify an unknown substance by using a density chart. 2. Less dense objects will float in a gas or liquid that is more dense. Ex. helium is less dense than air so helium balloons float. 3. Temperature can affect density. As you heat up an object, the molecules expand and move farther apart, decreasing density. 12

13 Review Prior to Density Definition (In words) Formula Units Equipment used in lab Volume Amount of space an object takes up. V= lwh V= r 2 h L, ml, cm 3 Graduated Cylinder Ruler Mass Amount of matter an object has X Kg, mg, g Scale Triple beam Denisty How much matter is squeezed into a given space. D= m/v Mass/volume g/ml g/cm 3 X Density One of the properties of solids, as well as liquids and even gases, is the measure of how tightly the material is packed together: density. Density is a measure of how much matter is squeezed into a given space; it is the amount of mass per unit volume: Density = Mass 1 Volume What happens to the density of a chocolate bar when you break it in two? The answer is, nothing. Each piece may have half the mass, but each piece also has half the volume. Density is not mass and it is not volume. Density is a ratio; it is the amount of mass per unit volume. A pure iron nail has the same density as a pure iron frying pan. The frying pan may have 100 times as many iron atoms and have 100 times as much mass, but its atoms will take up 100 times as much space. The mass per unit volume for the iron nail and the frying pan is the same. 13

14 Both the masses of atoms and the spacing between atoms determine the density of materials. Osmium, a hard bluish-white metallic element, is the densest substance on Earth, even though the individual osmium atom is less massive than individual atoms of gold, mercury, lead and uranium. The close spacing of osmium atoms in an osmium crystal gives it the greatest density. A cubic centimeter of osmium contains more atoms than a cubic centimeter of gold or uranium. One of the reasons gold was used as money was that it is one of the densest of all substances and could therefore be easily identified. A merchant suspicious that gold was diluted with a less valuable substance had only to compute its density by measuring mass and dividing by its volume. The merchant would then compare this value with the density of gold, 19.3 g/cm 3. Consider this: A man uses a gold nugget (with a mass of 47.9g and a volume of 3.00 cm 3 ), to buy a suit. Is the nugget pure gold? Compute its density in the box below. Density = Mass/Volume Density = 47.9 grams/ 3.00 cm 3 Density = g/cm 3 Calculating Density The formula for density is: Density = Mass Volume To calculate density first find the mass of the object, then find the volume. Divide mass by volume to determine the density. 7cm 1.5cm Example: a cylinder has a radius of 1.5 cm and a height of 7cm. Its mass is grams. 1. Calculate the volume. V = π r 2 h V = 3.14 x 1.5cm 2 x 7cm V = 49.5cm 3 2. Density = Mass/Volume Mass = g D = g / 49.5cm 3 D = 10.5 g/cm 3 14

15 Calculate the density of the box below: 15 cm 5 cm 6 cm Mass = 770 grams Density = Mass/Volume D= 770 grams / (15cm x 6cm x 5cm) D = 770g / 450cm 3 D = 1.7 g/cm 3 Which Element is this? Density is known as an property. Identifying Densities of common materials SOLIDS at 20 0 C Substance Density (g/cm 3 ) Osmium Platinum Gold Uranium Lead Silver Nickel 8.90 Copper 8.90 Steel 7.90 Iron 7.90 Zinc 7.10 Tin 5.60 Aluminum 2.70 Magnesium 1.7 Pine Wood 0.50 Balsa Wood 0.12 LIQUIDS at 20 0 C Substance Density (g/cm 3 ) Mercury 13.6 Carbon Tetrachloride 1.57 Chloroform 1.49 Sea Water 1.03 Water (4 0 C) 1.00 Olive Oil 0.92 Corn Oil 0.92 Turpentine 0.87 Methyl Alcohol 0.79 Ether 0.74 Gasoline 0.69 GASES at 0 0 C Substance Density (g/cm 3 Carbon Dioxide Oxygen Air Nitrogen Helium Hydrogen

16 Buoyancy Force that keeps something afloat Objects with lower densities will float on objects of greater densities. Man floating on Mercury Liquids and gases with different densities will separate out. Less dense substances will Float and more dense will. Sink Heat affects density Heat affects density. As a substance is heated its molecules move farther and farther apart. Less compact means less dense. Volume When heat expands an object Mass remains the same. increases but 16

17 What did Indy do wrong? 17