Chapter 5 · ApplicationsBuoyancy at workExplore online

Applications & Explore Online പ്ലവക്ഷമബലം

The buoyant force keeps INS Vikrant afloat off Kochi, takes a submarine down and brings it back up, holds your head above the water when you wear a life jacket on the Water Metro, lifts a hot-air balloon, lets a fish hover without effort, hides nine-tenths of an iceberg and catches watered milk at the milk society. Every lab below uses only the ideas of this chapter – and the computer works out every number from FB = ρ × V × g.

📖 The ideas behind every lab

Numbers used: g = 9.8 m/s², 1 kgwt = 9.8 N, water 1000 kg/m³, sea water 1025 kg/m³ (approx.), ice 917 kg/m³. Values marked “approx.” are typical values, not from the textbook.

1. Ships and the Plimsoll load line

A steel ship floats because of its shape. Its hollow hull pushes aside a huge volume of water, and it settles until the weight of the water it displaces equals its own weight (പ്ലവനതത്വം). Load more cargo and the ship sinks deeper – its draft, the depth of the hull under the water, increases. A ship must not sink too deep, so every cargo ship carries a load line, or Plimsoll mark, painted on its side: a circle with a line through it, and short lines marked S (load line in sea water) and F (in fresh water). The F line is higher because fresh water is less dense: the same ship sinks deeper in a river than in the sea. India’s first home-built aircraft carrier, INS Vikrant (the ship on the first page of this chapter), was built at Cochin Shipyard in Kochi. It displaces about 43 000 tonnes, so the sea pushes up on it with about 43 000 000 kgwt ≈ 4.2 × 108 N.

🚢 Ship lab: load the cargo, then sail from the river into the sea

The ship weighs 6000 tonnes empty. Its hull is treated as a box 100 m long and 20 m wide, so draft = volume of water displaced ÷ (100 m × 20 m). Heights are drawn three times taller than lengths so that you can see the draft change. 1 tonne = 1000 kg.

📝 In the exam this looks like: “A boat on a lake displaces 6000 kg of water. What is the buoyant force on it?” → buoyant force = weight of the water displaced = 6000 kgwt = 6000 × 9.8 = 58 800 N (and, since it floats, the boat also weighs 6000 kgwt). “A ship rises a little when it sails from a river into the sea – why?” → sea water is denser, so a smaller volume of it already weighs as much as the ship. “A ship rises after unloading at a port – why?” → its weight decreases, so it needs to displace less water to float (principle of floatation) – Let us assess Q3(b).

2. Submarines – ballast tanks

A submarine (അന്തർവാഹിനി) cannot change its shape, so the buoyant force on it, once it is fully under water, is fixed: ρsea × Vhull × g. Instead it changes its weight. It has ballast tanks. To dive, valves open and sea water floods into the tanks – the submarine becomes heavier than the water it displaces and sinks. To come up, compressed air blows the water out – it becomes lighter and the buoyant force pushes it up. With the tanks partly filled it can hover, its weight exactly equal to the buoyant force.

🫧 Submarine lab: flood and blow the ballast tanks

Example submarine: hull volume 2000 m³, mass 1750 tonnes with empty tanks, ballast tanks 400 m³; sea water 1025 kg/m³ (approx.). Fully under water the buoyant force is 2000 × 1025 = 2 050 000 kgwt, at any depth. The submarine moves slowly because the water drags on it.

📝 In the exam this looks like: “How does a submarine dive and surface?” → It takes sea water into its ballast tanks: its weight becomes greater than the buoyant force and it sinks. Compressed air pushes the water out: its weight becomes less than the buoyant force and it rises. Its volume, and so the buoyant force when fully under water, does not change. When weight = buoyant force under water, it stays at the same depth.

3. Life jackets and boat safety

Our bodies are only a little denser than water, so a person in water floats very low, with the mouth and nose under the surface – and in fresh water may slowly sink. A life jacket (ലൈഫ് ജാക്കറ്റ്) is filled with a very light foam (or air). It adds a large volume but almost no weight. The person and jacket together displace enough water for the buoyant force to equal their total weight while the head stays above the water. That is why life jackets are compulsory on boats – the Kochi Water Metro, ferries, houseboats on Vembanad lake and fishing boats.

🦺 Life-jacket lab: will your head stay above water?

A simplified model: average body density 1010 kg/m³ (approx.; it changes with breathing), body volume spread evenly over the height, foam jacket 100 kg/m³ (approx.) worn around the chest. The person floats where the buoyant force equals the total weight. For the mouth to stay out, the buoyant force from everything below the mouth must be at least the total weight.

⚠ Always wear a life jacket on any boat – even if you can swim – and fasten every strap. Never lean over a well or play near deep water; do water experiments in a bucket or tub, with an adult nearby.

📝 In the exam this looks like: Let us assess Q4 – “Life jackets are compulsory in boats. Explain on the basis of buoyant force.” → A life jacket is filled with very light material, so it adds a large volume with very little weight. The person and the jacket together displace more water; the buoyant force (the weight of the water displaced) becomes equal to their total weight while the head is still above the water, so the person floats and can breathe.

4. Balloons – buoyant force in air

Air is a fluid too, so it pushes up on everything in it with a buoyant force equal to the weight of the air displaced. For most things this is tiny compared with their weight. A balloon is different: it is big but very light. A helium balloon rises because helium is much less dense than air – the balloon weighs less than the air it pushes aside. A balloon filled with carbon dioxide (denser than air) sinks (Let us assess Q3a). A hot-air balloon rises because heated air expands and becomes less dense than the cooler air around it.

🎈 Balloon lab: toy balloon and hot-air balloon

Densities (approx.): air 1.2 kg/m³ at 20 °C, helium 0.17, carbon dioxide 1.84 kg/m³; rubber of the toy balloon 3 g. The hot-air balloon’s envelope holds 2800 m³ (approx.); hot air’s density is worked out from the gas laws: 1.2 × (273 + 20) ÷ (273 + T). The buoyant force on both balloons is the weight of the cool outside air they displace.

📝 In the exam this looks like: Let us assess Q3(a) – “Helium balloons rise in air but carbon dioxide balloons sink. Why?” → Helium is less dense than air, so the weight of the balloon is less than the weight of the air it displaces (the buoyant force) – it rises. Carbon dioxide is denser than air, so the balloon’s weight is greater than the buoyant force – it sinks. Also: “A helium balloon rises when released – which force pushes it up?” → the buoyant force of the air.

5. Fish and the swim bladder

Fish flesh and bones are a little denser than water. Most bony fish have a swim bladder (വായുസഞ്ചി) – a bag of gas inside the body. By putting gas into it or taking gas out, the fish changes its volume without changing its mass. A bigger bladder displaces more water, so the buoyant force grows and the fish rises; a smaller bladder lets it sink. With just the right amount of gas its average density equals the water’s and it hovers without effort – like a submarine, but by changing volume instead of weight.

🐟 Swim-bladder lab: rise, sink or hover

Example fish: mass 500 g, body without the bladder 467 cm³ (density about 1070 kg/m³, approx.); the gas itself weighs almost nothing. A sea fish needs a smaller bladder than a river fish of the same mass, because sea water is denser.

📝 In the exam this looks like: “How does a fish rise or sink in water?” → by changing the amount of gas in its swim bladder. More gas → more volume → more water displaced → buoyant force greater than its weight → it rises. Less gas → less volume → buoyant force less than its weight → it sinks. Its mass does not change; its average density does.

6. Ice and icebergs

Water is unusual: it expands when it freezes, so ice (917 kg/m³) is less dense than water and floats. By the principle of floatation, the fraction of a floating object under the liquid is ρobject ÷ ρliquid. For ice in sea water: 917 ÷ 1025 ≈ 0.89, so about 89 % of an iceberg (മഞ്ഞുമല) is hidden under the sea – only about one-tenth shows. That hidden part is what made icebergs so dangerous to ships such as the Titanic (1912). In fresh water a little more of the ice is under: 917 ÷ 1000 ≈ 92 %.

🧊 Iceberg lab: how much is under the surface?

The computer finds the water line by balancing the areas: it slides the line until the share of the shape below it equals ρobject ÷ ρliquid (a flat “slice” of an iceberg – every slice of a real iceberg floats the same way). If the object is denser than the liquid, the share would be more than 1 – it sinks.

📝 In the exam this looks like: “Why does ice float on water?” → The density of ice (917 kg/m³) is less than that of water (1000 kg/m³); it floats with part of it above the surface, where the weight of the water displaced equals its weight. “About what fraction of an iceberg is under sea water (densities 917 and 1025 kg/m³)?” → 917 ÷ 1025 ≈ 0.89, i.e. about 89 % (nine-tenths).

7. The lactometer at the milk society

At a village milk society (ക്ഷീരസംഘം) the staff dip a lactometer (ലാക്ടോമീറ്റർ) into every can of milk. It is a hydrometer (ഹൈഡ്രോമീറ്റർ) made for milk: a weighted glass float with a thin stem. It sinks until it displaces its own weight of milk, so it floats higher in denser milk; the number on the stem at the milk surface is the relative density (ആപേക്ഷികസാന്ദ്രത). Pure cow’s milk has a relative density of about 1.028–1.032 (approx.). Water (1.000) lowers it, so watered milk – an offence (മായം ചേർക്കൽ) – reads lower. Societies often write only the last two digits: a reading of “30” means 1.030.

🥛 Lactometer lab: add water to the milk

Example lactometer: mass 60 g, stem cross-section 0.5 cm². The depth it sinks to is worked out from “weight of milk displaced = weight of the lactometer”; that is why the gaps between the marks on its scale are not all equal, and why the values increase downwards. The relative density of a mixture is found from the share of each liquid by volume.

📝 In the exam this looks like: “Will a lactometer show the same reading in pure milk and in milk with water added? Why?” → No. Watered milk is less dense, so the lactometer sinks deeper and reads lower. “How can we find out whether water has been added to milk?” → measure its relative density with a lactometer; a reading below the pure-milk value shows added water. “Does the lactometer sink more in pure milk or in skimmed milk?” → in pure (whole) milk; removing the fat, which is lighter than water, makes skimmed milk denser.

✅ Check yourself

🌐 Explore online – resources hub

Everything in this guide works offline. The links below are extras – websites and simulations from trusted sources (PhET and others), grouped by topic. They need internet and open in a new tab, so you will not lose your place here. Ask a parent or teacher before you go online. The PhET simulations Buoyancy, Buoyancy: Basics and Density run directly in your browser – nothing to install. (The “Buoyant Force” simulation named in the textbook is the offline PhET copy on the KITE Ubuntu school laptops.)

Buoyant force – why things float or sink

🌐 Buoyant force – why things float or sink needs internet · opens in a new tab

Density of liquids and solids

🌐 Density of liquids and solids needs internet · opens in a new tab

Archimedes and his principle

🌐 Archimedes and his principle needs internet · opens in a new tab

Principle of floatation, boats and ships

🌐 Principle of floatation, boats and ships needs internet · opens in a new tab

Relative density

🌐 Relative density needs internet · opens in a new tab

Hydrometer and lactometer

🌐 Hydrometer and lactometer needs internet · opens in a new tab

Water safety and life jackets

🌐 Water safety and life jackets needs internet · opens in a new tab

More to explore

🌐 More to explore needs internet · opens in a new tab
🧭 Next

Now pull the whole chapter together: Summary & Quick Quiz ▶