That teaches better, that feels better. Mass Volume and Density. Over Betuwe College 2013 Page 1

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1 Mass Volume and Density Over Betuwe College 2013 Page 1

2 Contents 1 Volume Calculating volume Volume Symbols and conversion Mass Density The ratio table Proportional Calculating density Practice exercises VMBO - t Practice exercise HAVO/ATHENEUM Over Betuwe College 2013 Page 2

3 Density is a substance characteristic. It is the number of grams of 1 cm³ substance. In the chapter below we are going to look at the meaning of: volume; mass; density. 1 Volume Volume is the space taken up by substance. Volume can be calculated for a regular solid. With an irregular solid, the volume can be determined by using the immersion method. 1.1 Calculating volume. SOLID CUBE CONTENT Surface 6 a a 6a 2 Content a a a 3 a RECTANGULAR BLOCK Surface 2 l b 2 l h 2 b h Content l b h CYLINDER 2 Surface 2 r 2 r h Content r 2 h 1 4 d 2 h Over Betuwe College 2013 Page 3

4 SOLID CONTENT PYRAMID l Surface Surface area faces Content 1 h 3 Surface area CONE 2 2 Surface r (r h ) r l Content 1 2 h 3 r PRISM l b 2 h SPHERE Surface 4 r 2 d 2 Content r d 6 = Over Betuwe College 2013 Page 4

1.2 Volume 2 With an irregular solid, the volume can be determined by using the immersion method. V stone = V end V beginning 1.3 Symbols and conversion.

5 1.2 Volume 2 With an irregular solid, the volume can be determined by using the immersion method. V stone = V end V beginning 1.3 Symbols and conversion. Quantity V Unit cm³ 1 ml = 1 cm³ 1 L = 1 dm³ 1L = 10 dl = 100 cl = 1000 ml 1 m³ = 1,000 dm³ = 1,000,000 cm³ = 1,000,000,000 mm³ 1 m³ = 1 x 10 3 dm³ = 1 x 10 6 cm³ = 1 x 10 9 mm³ Over Betuwe College 2013 Page 5

2 Mass A substance consists of atoms. The mass (the number of grams) of an atom depends on the core particles. The mass of a substance is the same everywhere. This doesn t change.

6 2 Mass A substance consists of atoms. The mass (the number of grams) of an atom depends on the core particles. The mass of a substance is the same everywhere. This doesn t change. A cube of 100 grams on earth has also 100 grams of mass on the moon. The number of atoms is ultimately still the same. The term weight doesn t count here because weightlessness doesn t change the number of molecules. When we talk about grams or kilograms in physics, then the quantity is mass. Quantity mass m unit gram g Over Betuwe College 2013 Page 6

7 3 Density Density is the mass of one cubic centimetre of a substance If the volume and the mass are known, then the mass of 1 cm³ substance can be calculated. 3.1 The ratio table Mass in grams Volume in cm³ Proportional If the mass is twice as much, then the volume is also twice as much Mass : volume = constant Graphically this is a straight line through the origin. 3.3 Calculating density Volume V cm³ Mass m g Density ρ g/cm³ ρ = m V Example: m = 250 g V = 50 cm³ If there are two substances with different densities, the substance with the lowest density will float. At the same density, the substance mixes/floats. Think of a fish/submarine. ρ =? g/cm³ ρ = m V ρ = 250g 50cm 3 ρ = 5 g/cm³ Never take the average density of a mixture. Add up the volume and add up the mass. Calculate the density. Over Betuwe College 2013 Page 7

8 4 Practice exercises VMBO - t. 1) Erica wants to investigate whether iron is heavier or lighter than aluminium. She can do this by weighing pieces of iron and aluminium that: a. are the same size. b. are equally heavy. 2) By density is meant: a. The volume of one gram of a substance. b. The volume of 1 cm 3 substance. c. The mass of 1 g substance. d. The mass of 1 cm 3 substance. 3) Marijke says: You can recognise a substance by it s density. Willem says: Density is a substance characteristic. Who is right? a. Both. b. Neither. c. Marijke. d. Willem. 4) What is the formula for calculating density? a. Density = volume ρ = V mass m mass b. Density = ρ = m Volume V c. Density = mass Volume ρ = m V d. Mass = density m = ρ Volume V 5) Fill in : a. You measure the density of a substance in per.. and you write it as / b. Aluminium has a smaller/equally large/larger density than steel. Over Betuwe College 2013 Page 8

6) Density is a substance characteristic. This doesn t change. You can look up the density in a table. You can find density in table 15 of the Binas. Density Order a. Complete the table.

9 6) Density is a substance characteristic. This doesn t change. You can look up the density in a table. You can find density in table 15 of the Binas. Density Order a. Complete the table. Take care that the Metal in g/cm metals are given in order of density. number (You can recognise the metals in the Binas because the specific resistance in the last column is smaller than one) Aluminium 2.7 b. What is the lightest metal? c. What is the heaviest metal? 7) You can calculate density using. Divided by 8) In the pictures below there are three objects, A, B and C Calculate the density of the objects. mass 6,0 g A. Density = ρ = m = = Volume V 5,0 cm 3 g/cm3 mass B. Density = ρ = m = g = Volume V cm 3 g/cm3 C. Volume = l b h = cm cm cm = cm 3 Density = mass Volume ρ = m V = g cm 3 = g/cm3 A mass = 6.0 g Volume = 5.0 cm 3 B mass = 27 g Volume = 10 cm 3 C mass = 80 g Volume = cm 3 h=4.0 cm l=1.5 cm b=1.5 cm Over Betuwe College 2013 Page 9

10 9 a Calculate the density of the substances in figure 9 mass A. Density = ρ = m = = g/cm 3 Volume V B. Volume = end position initial position =.... =.. cm 3 ρ = m V = = g/cm3 C. Volume =.... =.. cm 3 ρ = m V = = g/cm3 D mass = 26 g E mass = 68 g F mass = 63 g Volume = 10 cm 3 initial position = 53 cm 3 initial position = 41 cm 3 end position = end position = Volume = Volume = b) Write down for each object what kind of substance it could have been made of. Search in the Binas from witch materials the objects are made Object D is made of Object E is made of Object F is made of Over Betuwe College 2013 Page 10

10 With a graduated cylinder and scales (and a little calculating) you can determine the density of a liquid (figure 10). a. Read off how great the volume and the mass of the liquid are: volume = ml mass = g b.

Which substance has the greatest density? How can you tell that? Two blocks keep each other in balance. Extra The density of water and ice 12 An ice block is 3.0 cm long, 2.0 cm wide and 1.

11 10 With a graduated cylinder and scales (and a little calculating) you can determine the density of a liquid (figure 10). a. Read off how great the volume and the mass of the liquid are: volume = ml mass = g b. Using these details, calculate the density of the liquid. c. What liquid could this be? Use table 15 of your Binas 11 The blocks A and B are made of different substances. Which substance has the greatest density? How can you tell that? Two blocks keep each other in balance. Extra The density of water and ice 12 An ice block is 3.0 cm long, 2.0 cm wide and 1.5 cm high. The mass of the ice block is 8.1 g. a. Calculate the density of the ice with these details b. Does the outcome make sense with what it says in the handbook? Explain your answer. Over Betuwe College 2013 Page 11

12 5 Practice exercise HAVO/ATHENEUM 1HA About density a Explain why we call density a substance characteristic. b Give the formula of density. 2HA Density in another unit Janna has a chunk of nickel with a volume of 1.3dm 3 and a mass of 11.6 kg. a How many cm 3 is equal to 1.3 dm 3? b How many g is equal to 11.6 kg? c Calculate the density of nickel in g/cm 3. Now calculate in the same way the density of the three following substances in g/cm 3 : d Magnetic steel, from which there is a horseshoe magnet that has a volume of 135 cm 3 and a mass of 0.93 kg. e A wooden chess piece with a volume of 1458 mm3 and a mass of 1250 mg. f Fuel oil with a mass of tonnes standing in a barrel of 159 litres. (1 tonne = 1000kg) 3HA How many types of wood? Marnix has a number of wooden toys. He wants to investigate how many different types of wood the toys are made of. To do that he determines the mass and volume for each toy. This gives the following results: a Volume (cm 3 ) mass (g) Put these values into a diagram, with volume on the x-axis and mass on the y-axis. Over Betuwe College 2013 Page 12

5HA The wooden block here on the right has a mass of 160 g. Calculate the density of the wood from which the block has been made.

13 b Using the diagram, say how many types of wood have been used for Marnix s toys. 4HA The water in a measuring glass rises, like in the image on the right, when you drop the tin horse into it. Calculate the mass of the tin horse. 5HA The wooden block here on the right has a mass of 160 g. Calculate the density of the wood from which the block has been made. 6HA Tjeerd has determined the mass and volume of five brass objects. He has collected the results of his measurements in the table below. a) Put Tjeerd s measuring results into a graph. b) Read off from this graph how great the mass is of a brass object with the volume of 5.0 cm 3. Over Betuwe College 2013 Page 13

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15 7HA Jantje has a piece of wood in his hands. If he drops the piece of wood into a graduated cylinder with water in, it sinks. The level in the graduated cylinder rises by 15 ml to 85 ml. a) Calculate the initial position of the water before the wood was placed in it. b) What type of wood was the block made out of? c) Calculate the mass of the block of wood. 8HA How heavy is sugar water on the stomach? a If you dissolve a little sugar in water, the volume of the mixture (sugar water) seems to be just as great as the volume of the water. Carla mixes 60.0 cm 3 water with 4.0g sugar. Explain how it is possible that the volume of the fluid doesn t change, even though a substance has been dissolved into it. Carla has to calculate the density of the sugar water. For this she makes first of all two drawings: one drawing of the situation before the dissolving and one from the situation after the dissolving. She puts the details in both drawings and afterwards calculates the density as required. B HA Produce the same drawings as Carla. C A Calculate the density of the sugar water. 9A a b c Oil mixture John has 10 dm 3 petrol and wants to mix oil through it. He has to mix at 1 to 25, that means one part oil to 25 parts petrol. The oil has a density of 0.80g/cm 3, the petrol 0.75 g/cm 3. How many cm 3 of oil does John need? Give a reasoned estimate for the density of the petrol-oil mixture. Calculate the density via the mass of the petrol mass of the oil total volume. John uses so little oil that when mixing it the volume of the petrol doesn t change. Over Betuwe College 2013 Page 15

16 10A On top of a well there is a round iron lid with a surface area of m² and a thickness of 3.0 cm. Calculate the mass of the lid. 11A There are 32 l petrol in a can. The whole weighs 23.8 kg. Calculate the mass of the empty can. 12A A measuring glass has a mass of 235 g. Calculate the total mass of the measuring glass if this is filled with milk up to the measuring line of 85 ml. The density of the milk is g/cm³ 13A A cylindrical measuring glass has a diameter of 6.0 cm. It is filled with 0.55 kg of mercury. Calculate how high the liquid comes to in the measuring glass. Over Betuwe College 2013 Page 16

Physics. Practical 5: Density. Practical Objective. Content Objective. Apparatus. Your teacher may watch to see if you can:

Physics. Practical 5: Density. Practical Objective. Content Objective. Apparatus. Your teacher may watch to see if you can: The density of a substance is the mass of a unit volume of that substance. Almost all substances are most dense when they are solids and least dense when they are gases. The arrangement of particles can