4A Density

1 - Introduction

Every substance and material consists of very small particles.
Those particles are not equally close to each other and are not all the same.
In one fabric they are closer together (or have a different size) than in another fabric.
We call this phenomenon the: density.

You can calculate density.
For this you need two things in advance:

mass
volume

2 - Mass

Mass is the amount of material that makes up an item.
You measure mass with a balance.
Below 2 types are shown, an 'ordinary' manual and an electronic balance.

The symbol for the quantity mass is the lowercase m.
The unit comes after the number.
The unit of mass is kg (1 kilogram = 1000 g).
The following is used for small masses: g (gram)

Example: m = 30 kg
Herein: m is the quantity mass
kg the unit.

3 - Volume

Volume indicates how large something is (how much space something takes up).

Below you will learn how to determine the volume of

a regular object (for example, a beam)

and

an irregular object (for example, a stone).

4 - Volume - regular subject

You measure the length, width and height of a regular object with a ruler.

You then use the formula V = l x w x h to calculate the volume.

The V is a capital letter; the l, b and h are lowercase letters.

5 - Measuring with caliper

You can use a ruler to measure sizes.
You can measure much more accurately with a: caliper gauge.

If you measure with a caliper you can measure with more numbers behind the comma.
For measuring, you mainly use the measuring jaws, the ruler and the vernier.

Measure to 1 decimal

Read how much on the ruler
whole millimeters
the 0 of the vernier is.
In this example: 24 mm.

Kijk nu welke streepje van de nonius
precies recht tegenover
een steepje op de liniaal staat.
In dit voorbeeld is dat
bij het getal 7 op de nonius.
De totale maat is dus: 24,7 mm

Click here to see the entire animation.

Watch the video explaining the caliper reading.

Answer the questions below.

Measure to 2 decimals

If the line between 2 nonius numbers is exactly opposite a line on the ruler, read the measure to two decimal places.
In this example: 20 mm + 0.35 mm = 20.35 mm

Answer the following questions. Read the numbers to 2 decimal places.

If you want to practice extra, you can do that by clicking here.

With a caliper you can measure in different ways.
Below you can see some examples.

6 - Volume - irregular object

With an irregular throw you use the: immersion method.

Fill a measuring glass to a certain height (eg 50 cm³)
Immerse the stone in the measuring glass.
Read again the position of the fluid (eg 70 cm³)
The volume of the stone is:

V_brick= 70 cm³ - 50 cm³ = 20 cm³

7 - Density

Each substance consists of very small particles that together form the mass of the substance.
These small particles are called molecules.
In general you can say:

The closer the molecules are to each other, the greater the density of the substance
The farther away the molecules are from each other, the smaller the density of the substance.

In the case of a solid, the molecules are close to each other >> high density.

With a liquid, the molecules are further apart from each other >> lower density.

With a gas, the molecules are 'far' from each other >> lowest density.

Note: there are exceptions to this rule because molecules of different substances also have a different structure.

You can calculate density, mass and volume with the formula:

ρ = m / V (ρ is a greek letter and you pronounce 'rho')

In this is:

ρ the symbol for density	the unit is:	g/cm³	or	kg/dm³
m the symbol for mass	the unit is:	g	or	kg
V the symbol for volume	the unit is:	cm³	or	dm³

Example 1:
Calculate the density if m = 40 g and V = 10 cm³.

F:	ρ = m / V
i:	ρ = 40 / 10
A:	ρ = 4 g/cm³

Example 2:
Calculate the mass if ρ = 4 g / cm³ and V = 10 cm³.

F: ρ = m / V
i:       4 = m / 10
A:    4 × 10 = m    (/ 10 becomes × 10 at the bottom of the fraction. 'Divides' becomes 'times')
   m = 40 g

Example 3:
Calculate the volume if ρ = 4 g / cm³ and the mass = 40 g

F:          ρ = m / V
i:    4 = 40 / V
A:    4 × V = 40    (/ V becomes × V at the bottom of the fraction. 'Divides' becomes 'times')
      V = 40 / 4 (Leave greatness. 'Times 4' becomes 'divide by 4')
      V = 10 cm³

8 - Density: table

9 - Density: exercices

1. a. Calculate the density of a substance with a mass of 130 g and a volume of 50 cm³.
b. What substance is this?

2. a. A liquid has a mass of 168 g and a volume of 200 cm³.
Calculate the density of this liquid.
b. Which liquid is this?

3. a. A balloon measuring 400 cm³ contains 71.2 g of gas. Calculate the density of the gas.
b. What gas is the balloon filled with?

____

4. Calculate the mass of a 25 cm³ iron object.

5. A brick is 120 cm³ in size. Calculate the mass of the stone.

6. Calculate the mass of 80 cm³ of alcohol.

____

7. The mass of a copper object is 403.2 g. Calculate the volume.

8. Angela has a bracelet of 42 g silver. Calculate the volume of the bracelet.

9. Calculate the volume of 1224 g of gasoline.

___

10. An oak board is 1.2 m long, 3 dm wide and 6 cm high.
a. Calculate the volume of the bar.
b. Calculate the mass of the beam.

11. The bar next door is made of pine wood.
Calculate the mass of this beam in g and kg.

12. A piece of nickel is 28 cm long, 3 cm wide and 8 mm high.
a. Calculate the volume of the nickel piece.
b. Calculate the mass of the nickel piece.

___

13. A ship illegally discharges 200 liters of fuel oil at sea.
a. Calculate the mass of the fuel oil discharged.
b. Why does fuel oil float on seawater?
c. What drives fuel oil the best: water or seawater? Why?

14. How do you measure the mass?

15. How can you measure the volume of a liquid?

16. How can you determine the volume of a regular item?

17. A measuring glass is filled to 50 mL.
One puts a brick in the measuring glass
causing the liquid to rise to 78 mL.
a. Calculate the volume of the brick in cm³.
b. Calculate the mass of the brick.

18. An empty measuring glass has a mass of 125 g. 60 mL of liquid is poured into the measuring glass.
The measuring glass with the liquid in it is weighed. It now weighs 172.4 g together.
a. Make a drawing of the empty measuring glass and write in the mass.
b. Make a drawing of the filled measuring glass next to it and write the mass.
c. Calculate the mass of the liquid poured into the measuring glass.
d. Calculate the density of the liquid.
e. Which liquid has been poured into the measuring glass?

19. In the Care and Welfare Department a medicine is made by weighing the mass of a substance on a balance.
a. How many grams does this substance weigh?
The volume of the fabric is 73.25 cm³.
b. Calculate the density of the drug.

20. You should drink well during intensive exercise, but you do not want to carry too much mass with you. You have a 200 ml bottle for your drink.
If you want to lift as little mass as possible, do you have to fill the bottle with water or with an energy drink with a density of 1.15 g / cm³? Why?

21. There is milk in a measuring cup. See the image on the right.
The density of milk can vary slightly.
a. Calculate the maximum mass of the milk.
b. Calculate the minimum mass of the milk.

22. See the image on the right.
On a scale (balance) is a piece of rubber (mass in g).
Calculate the volume of the rubber.

10 - PR: Density - measure and calculate

In this practical you will calculate the density of different materials in different ways.

Necessities:
- balance with mass block
- measuring glass 100 mL
- caliper
- regular metal and plastic objects of the same size
- irregular object: "nut"
- cylinder
- spirit
- metal hook

Execution of the test, measurement data and calculations.

1. Balance the balance.

The "grams" from the mass block are either on the balance or in place in the mass block.

Density calculation of a liquid

2. Determine the mass of the empty measuring glass.
3. Determine the mass of the measuring glass filled with 50 mL of spirit.
4. Calculate the mass of the spiritus with this.
5. Calculate the density of the spirit.

Calculate density of two regular (beam-shaped) objects

6. Determine the mass of the regular metal object.
7. Determine (using the caliper gauge) the length, width and height of the metal object.
8. Calculate the volume of the metal object with the formula.
9. Calculate the density of the metal.

10. Determine the mass of the regular plastic item.
11. Determine (using the caliper gauge) the length, width and height of the plastic object.
12 Calculate the volume of the plastic object with the formula.
13. Calculate the density of the plastic.

14. These two regular objects are almost the same size, yet their mass is very different.
Explain how this is possible.

Density calculation of a cylinder

15. Determine the mass of the metal cylinder.

16. How much spirit is there in your measuring glass now?

To determine the volume for the immersion method, use the hook to lower the object into the spirit.
17. Determine the volume of the spirit with the cylinder.
18. Calculate the volume of the cylinder.

19. Calculate the density of the cylinder.
20. From which material can this cylinder be made according to the density table.

Density calculation of the metal nut

21. Determine the mass of the metal nut.

22. How much spirit is there in your measuring glass now?

To determine the volume for the immersion method, use the hook to lower the object into the spirit.
23. Determine the volume of the spirit with metal nut.
24. Calculate the volume of the metal nut.

25. Calculate the tightness of the metal nut.
26. From which material can the metal nut be made according to the density table.

Compare the answer for assignments 19 and 20 with the answer for assignments 25 and 26.
27. What do you notice?
28. Explain the answer to the previous question.

11 - Density - applet

In this lesson you will do a digital practical about DENSITY based on assignments.

Do you use an iPad? Then open this exercise in the Puffin browser .

Click on the image to the right to open the applet.

1. The volume of the block of wood = 5.00 L.
How large is the volume of the block of wood in dm³.
2. Calculate the density of the block of wood.

At the top left, select Material: Ice.
3. Calculate the volume of the ice in dm³.
4. Show with a calculation that the mass of this ice block is 4.6 kg.

Select top left behind Material: Styrofoam.
5. Use a calculation to show that the polystyrene volume is 5 dm³. Use the density indicated in the applet in your calculation.

At the top right click on: Same mass.
The four blocks all have the same mass.
6. Why are the four blocks the same weight, but not the same size?
7. Which block do you think has the highest density: the yellow or the red block? Explain your answer.

At the top right click on: Same volume.
The four blocks drawn are the same size, but not the same weight.
8. What do you have to do to determine the density of the yellow block?
9. Calculate the volume of the yellow block.
10. Calculate the density of the yellow block.

11. Calculate the volume of the red block.
12. Calculate the density of the red block.

At the top right click on: Same density.
13. Calculate the density of the green block.

Click at the top right on: Mystery.
14. Calculate the density of the yellow block (A).
15. Calculate the density of the red block (D).

4B Law of Archimedes

1 - Eureka: I've got it!

In this chapter you will learn the Law of Archimedes.
This is a famous physics law that explains, among other things, why a heavy metal ship floats while a much less heavy solid piece of metal actually sinks.

The famous Greek inventor Archimedes devised this law when he was in the bath, and he suddenly got inspiration when he saw the water rise from his bath.
That is why he hurriedly ran through Athens to his laboratory to prove with experiments and calculations that his thought was good.
While running, he shouted loudly: Eureka !! Eureka !! which means: I have it !! I've got it!!

Archimedes distinguished 3 different situations:

Sinking: - then the object sinks into the liquid.
- the entire object is immersed in the liquid.

Floating: - then the object floats somewhere between the bottom and the surface.
- the entire object is immersed in the liquid.

Hovering: - the object floats on the surface.
- a part of the object protrudes above the liquid.

2 - Law of Archimedes - applet

Do you use an iPad? Then open this exercise in the Puffin browser .

You will conduct research into the: Law of Archimedes

1. Click on the image to open the applet.

2. Set the settings at the bottom left of the applet as shown opposite.
Check mark for: Gravity on.
Check mark for: Float on.

Checkmark: Masses off.
Check for: Size of the forces.

3. Place the wooden block on the scale.
What is the gravity (= weight) of the wooden block?

4. How many liters of water is in the container?

5. Put the wooden block in the water container.
Does the wooden block sink, float or float?

6. The water in the container has become higher (volume is larger).
That is because the block of liquid pushes away.
Calculate the volume of the pushed (displaced) fluid.

7. How large is the upward force?

8. What conclusion can you draw from this study about the upward force?
Begin your answer with: Als een voorwerp drijft dan ...

9. Remove the wooden block from the bin.

10. Determine the gravity (= weight) of the stone block?

11. Put the stone block in the water container.
Does the stone block sink, float or float?

12. The water in the container has become higher (volume is larger).
Calculate the volume of the fluid being moved.

13. How large is the upward force?

14. What conclusion can you draw from this research?
Begin your answer with: If an item sinks then ...

15. Remove the stone block from the container.

16. Place the liquid under the applet: Oil.

The density of water is 1 g / cm³.
The density of oil is rounded 0.92 g / cm³.
So oil is slightly lighter than water per cm³.
You are now going to investigate what influence a smaller density has on the upward force.

17. Put the wooden block in the oil container.
Does the wooden block sink, float or float?

18. Calculate the volume of the fluid being transferred.

19. How large is the upward force?

20. After this investigation you can say something about it

volume of the fluid being moved
and about the upward force.

a. What conclusion can you draw from this research about the volume of the fluid being transferred?
b. What conclusion can you draw from this research on upward force?

21. Remove the wooden block from the bin.

22. Put the stone block in the oil container.
Does the stone block sink, float or float?

23. Calculate the volume of the fluid being transferred.

24. How large is the upward force?

25. After this investigation you can say something about it

volume of the fluid being moved
and about the upward force.

a. What conclusion can you draw from this research about the volume of the fluid being transferred?
b. What conclusion can you draw from this research on upward force?

26. Click in the applet at the top left on:

27. Set the settings in the lower left corner of the applet as shown opposite.
Check mark for: Gravity on.
Check mark for: Float on.

Checkmark: Masses off.
Checkmark for: Size of the forces on.

You are now going to investigate what influence it has when an object and the liquid have an equal density.

In the applet you can see on the top left that the density of wood is 0.4 kg / L.

We prefer to use the unit for density: g / cm³.
You can convert kg/L to g/cm³.
A liter (L) is equal to a dm³ which means you can say: 0.4 kg/L = 0.4 kg/dm³.
A kg equals 1000 g and a dm³ equals 1000 cm³.
Since you can divide 1000 by 1000 you can say 0.4 kg/dm³ = 0.4 g/cm³.

28. Click at the bottom of the applet in the area where the number represents the density of the liquid.

29. Change the number 1.00 by the number 0.4 (In this applet, type 0 point 4 instead of 0 comma 4).

You have now made the density of the liquid equal to the density of the object (the wooden block).

30. Place the block on the scale. What is the weight of the block?

31. Place the wooden block in the container with liquid.
The block must not touch the bottom!
Does the wooden block sink, float or float?

32. Calculate the volume of the fluid being transferred.

33. How large is the upward force?

34. Place the block on the scale that is at the bottom of the bin.
a. What value does the scale indicate?
b. Give an explanation for this.

35. After this investigation you can say something about it

volume of the fluid being moved
the upward force.
a. What conclusion can you draw from this research about the volume of the fluid being transferred?
b. What conclusion can you draw from this research about the upward force of an object that is floating?

In summary, the Law of Archimedes is:
the upward force is equal to the weight of the amount of fluid displaced.

3 - Weight of the fluid being moved

4 - Crown of Syracuse (* bonus)

5 - PR: Opwaartse kracht

Particles, Temperature and phase transition

Colofon
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Marc Molenaar

Laatst gewijzigd

2019-04-07 00:40:16

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4vtto - 4 Substances and Particles

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2019-04-07 00:40:16

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