Density and Buoyancy

1. Density and Buoyancy

2. Density and Buoyancy • Buoyancy is the tendency to rise or float in water or air. • The upward force exerted on objects submerged in fluids is called buoyant force. • The buoyancy of a fluid is related to a fluid’s density- the amount of mass in a certain unit volume of a substance.

3. Density and the Particle Theory • Density can be described as the “crowdedness” of particles that make up matter. • In scientific terms, density is the amount of a substance that occupies a particular space. When you describe a substance as being “heavy” or “light”, you are talking about density.

4. Density and the Particle Theory • According to the particle theory, different substances have different sized-particles. The size of the particles determines how many particles can fit into a given space. Therefore, each substance has a unique density, based on particle size.

5. Density of solids, liquids, and gases • How is the density of a substance related to the substance’s physical state? Imagine filling a film container with water, and then another with water vapour. • Liquid water and water vapour are the same substance and therefore have particles of the same size. According to particle theory, gas particles have more space between them than do liquid particles.

6. Density of solids, liquids, and gases • The water vapour in the container would have fewer particles than the liquid water. • We can conclude that the density of the water vapour is less than the density of liquid water.

7. Stop and Think: • Imagine you were to fill three balloons to the same size: one with plaster, which would harden into a solid; the second with water, a liquid; and the third with air, a mixture of gases. • Use the particle theory to try to explain how and why the density of the substances inside each balloon varies.

8. Density of solids, liquids, and gases • How are density and state of matter related to the physical properties of a substance? • Solid objects can move easily through liquids and gases. • According to the particle theory, the fluid properties of water and of air allow water particles and air particles to move out of the way of the non-fluid bodies of animals.

9. Density of solids, liquids, and gases • When an object moves through a fluid, it pushes particles apart and moves between them. Particles in a solid cannot be pushed apart. • Attractive forces among the particles of a solid are stronger than those between fluid particles and thus the particles in a solid cannot be pushed apart.

10. Density of solids, liquids, and gases • If you were to step onto the surface of a lake, the water would not support your foot. Instead, your foot would continue to fall through the water, pushing the water particles out of the way. • Liquids cannot support objects in the same way that solids can, because the particles of a liquid move apart easily, allowing a dense, solid object, such as your foot, to pass through the liquid.

11. Density of solids, liquids, and gases • Similarly, you can’t walk on air, because gases are even less dense than solids or liquids. • When you move through air, you are moving through mostly empty space. You do not have to move as many particles of air out of the way as you do in water. • This explains why running through air is much easier and faster than running through water. In general, gases are less dense than liquids.

12. Density of solids, liquids, and gases • As temperature increases, a substance will change from solid, to liquid, to gas. • The particle theory states that the particles of a substance spread out as they gain energy when heated. • Thus, the particles take up more space, which means that the density of the substance decreases.

13. Density of solids, liquids, and gases • It is almost always true that for each pure substance (like gold), the density of its solid state is greater than the density of its liquid state. • The substance’s solid state and liquid state are, in turn, denser than its gaseous state.

14. Density: How are mass and volume related? • How can you measure the density of a substance? • You could determine a substance’s density if you knew how much of the substance occupies a certain space.

15. Density: How are mass and volume related? • To find out how much of the substance occupies a space, you can first of all measure the mass of the substance. • Mass is the amount of matter in a substance. • Volume is a measurement of the amount of space occupied by the substance.

16. Density: How are mass and volume related? • There are two ways to determine the volume of a solid. • A regularly shaped object (like a block of wood) can be measured and the volume can be determined using the mathematical formula v=l x w x h.

17. Density: How are mass and volume related? • An irregularly shaped object, like a strawberry, can be found by measure the volume of water that spills out of an overflow can. • The volume of a liquid can be measured by using a measuring cup or graduated cylinder.

18. Density: How are mass and volume related? • The volume of a gas can be determined by measuring the volume of the container that holds it. • The greatest amount of fluid that a container can hold is called its capacity. • Capacity is usually measured in litres or millilitres.

19. Density: How are mass and volume related? • Mass and weight are not the same. Weight is the force of a gravity exerted on an object. • Force is a push or a pull, or anything that might change the motion of an object. • Gravity is the natural force that causes an object to move toward the centre of the Earth.

20. Density: How are mass and volume related? • All forces, including weight, are measured in newtons (N). • The pull of gravity everywhere on Earth’s surface is essentially the same. • On Earth, gravity pulls an object with a downward force of 9.8 N for every kilogram of its mass.

21. A formula for density

22. Stop and Think: • The mass of an object depends on the amount of matter that makes up the object. • The weight of an object changes as gravitational forces change. • The pull of gravity on the Moon is about one sixth of Earth’s gravity (1.6N/kg). On the Moon, what would your mass be? What would your weight be?

23. A formula for density

24. A formula for density • As long as the temperature and pressure stay the same, the mass-to-volume ratio, or density, of any pure substance is a constant, which means it does not change.

25. Buoyancy: The Anti-Gravity Force • Many people enjoy playing in the water because there are many things you can do in water that you cannot do on land. • For example, it’s much easier to do a handstand in the water than it is on land. • The water exerts an upward force that helps support you when you do a handstand.

26. Buoyancy: The Anti-Gravity Force • Buoyancy refers to the ability of a fluid to support an object floating in or on the fluid. • The particles of a fluid exert a force in a direction opposite to the force of gravity. The force of gravity pulls down toward the centre of Earth. • Buoyant force- the upward force on objects submerged in or floating on fluids pushes up, away from Earth.

27. Buoyancy: The Anti-Gravity Force • Like all other forces, buoyant force is measured in newtons (N). • Floating occurs when an object does not fall in air or sink in water, but remains suspended in the fluid. • People can’t walk on water, but many of us can swim in water, and we can float on the surface of water.

28. Buoyancy: The Anti-Gravity Force • People can also float on the surface of the water in a boat. • Hot air balloons can be suspended in the air for long periods of time. • Why do you think fluids can support certain objects?

29. Buoyancy: The Anti-Gravity Force • How can people travel in the air and on water if the density of their bodies is greater than the density of both these fluids? • Why don’t we sink? • It seems that water can support objects that have densities greater than water-as long as the weight of the object is spread over a large enough area.

30. The Hibernia oil rig has a mass of over 14 000 tonnes, but it floats on the water.

31. A straight pin has a mass of less than 1 g. However, the pin sinks when placed in water.

32. Average Density • Ships can be built of steel (density of 9g/cm3) as long as they have large, hollow hulls. • A large, hollow hull ensures that the average density of the ship (that is, the total mass of all substances on board divided by the total volume) is less than that of water.

33. Average Density • Similarly, life jackets are filled with a substance of very low density. Thus, life jackets lower a person’s overall density, allowing the person to float.

34. Benefits of Average Density • Average density is useful because it enables objects that would otherwise sink- such as large ships and oil rigs- to float. • Average density also helps floating objects to sink.

35. Benefits of Average Density • For example, most fish have an organ called a swim bladder (also called an air bladder). • This organ contains a mixture or air and water. • The fish’s depth in the water depends on how much air is inside the air bladder.

37. Benefits of Average Density • As the amount of air decreases, the fish sinks lower. As the amount of air increases, the fish rises closer to the surface. • This depth-control structure has been adapted in the submarine, allowing the submarine’s crew to adjust its depth underwater.

38. Benefits of Average Density • The buoyant force of air is much smaller than the buoyant force of water. • Although air particles are extremely far apart, they are still close enough together to support some objects.

39. Benefits of Average Density • The Goodyear blimp is one of the largest airships in the world. • It can carry people as well as the substances that make up its structure. • This giant airship is filled with helium gas, the second lightest gas that exists.

40. Benefits of Average Density • An airship such as a blimp can float because its mass is relatively small compared to its enormous volume. Therefore, its average density is slightly less than the density of the air surrounding it. Ocean-going ships, hot-air balloons, and blimps all have huge volumes. • The relationship between the size of an object and the buoyant force exerted upon it was established long ago by a scholar named Archimedes.

41. Archimedes’ Principle • The Greek scientist Archimedes made a brilliant discovery around 212 B.C.E. • Hiero II, the ruler of Syracuse, suspected that his crown had not been made with pure gold, and it was up to Archimedes to determine whether or not the goldsmith was honest.

42. Archimedes’ Principle • Archimedes knew that all he had to do was determine whether the density of the crown matched the density of the gold. • Remember, the formula for density requires only mass and volume.

43. Archimedes’ Principle • Archimedes could easily measure the mass of the crown with a balance, but how could he measure something as irregularly shaped as a crown? • Archimedes solved the problem while at the public baths. He noticed that when he sat in the nearly full tub, the tub overflowed. • Archimedes realized that a solid object can displace water out of a container.

44. Archimedes’ Principle • Archimedes reasoned that the water displaced in the tub must have exactly matched the volume of his body. • To find the volume of the crown, Archimedes submerged it in water, and measured the water that spilled out of the container.

45. Archimedes’ Principle • Archimedes applied his new ideas to another property of fluids. • He believed that the displaced fluids held the key to whether the object placed in the fluid would sink or float. • He wondered why he would sink if he got into a bathtub, but he would float if he stood in a boat on the water.

46. Archimedes’ Principle • He concluded that the amount of buoyant force that would push up against the object immersed in the fluid would equal the force of gravity (the weight) of the fluid that the object displaced.

47. Archimedes’ Principle • The particle theory can explain why this was a reasonable conclusion. • If the water in a container is still, or at rest, then the water particles are neither rising nor sinking. An object immersed in a fluid such as water doesn’t rise or sink if the amount of force pulling down (gravity) equals the amount of force pushing up (buoyancy).

48. Archimedes’ Principle • This condition is known as neutral buoyancy. • Therefore, the water particles in the lower part of the container must be exerting a buoyant force equal to the weight, or force of gravity, of the water above it.

49. Archimedes’ Principle • If 1L of water is displaced, the object replacing it would have the same volume (1L), but might have a different weight than the 1L of water. If the object is heavier than the water, then the weight of the object will be a force greater than the buoyant force that had supported the displaced water. Therefore, the object will sink. • If the object is lighter than the displaced water, the object will rise to the surface and float.