11.4 Upthrust and Flotation

A free GCSE Physics lesson for AQA (8463) from OBA School: what upthrust is, what causes it, and why objects float or sink. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

• Describe upthrust as the upward force a fluid exerts on an object in it, and measure it with a newton-meter
• (Higher tier) explain that upthrust is caused by the pressure on the bottom of an object being greater than on the top
• (Higher tier) state that the upthrust on an object equals the weight of fluid it displaces, and use this in calculations
• Explain floating and sinking in terms of weight and upthrust, and in terms of density
• Explain why a ship floats lower as it is loaded

Key words

• Upthrust: The upward force on an object that is partly or totally in a fluid.
• Displace: To push fluid out of the way. The volume displaced is the volume of the object below the surface.
• Immersed: Under the surface of a fluid. Fully immersed (submerged) means completely underneath.
• Apparent weight: The reading on a newton-meter when the object is in a fluid: weight − upthrust.
• Density: Mass per unit volume, ρ = m / V, in kg/m³. Water is 1000 kg/m³.
• Float: Stay at rest at the surface, with the upthrust equal to the weight.

Upthrust and how to measure it

Objects feel lighter in water because the water pushes up on them. This upward force from a fluid is called upthrust. Gases cause upthrust too, which is why helium balloons rise.

Hang an object from a newton-meter in air: the reading is its weight. Lower it into water: the reading falls. The difference is the upthrust. As more of the object goes under, the reading keeps falling (upthrust increasing) until it is fully immersed. After that the reading stays the same, however deep it goes.

Key fact: upthrust = weight in air − apparent weight in the fluid

What causes upthrust? (Higher tier)

Pressure in a fluid increases with depth. The bottom of a submerged object is deeper than its top, so the water pressure on the bottom is greater. This gives a bigger upward force on the bottom than the downward force on the top. The forces on the sides cancel out. The resultant of all these forces is the upthrust, acting upwards.

Worked example: upthrust from pressures

A cylinder of cross-section 0.010 m² has its top 0.20 m and its bottom 0.50 m below the surface of water.
pressure on top = 0.20 × 1000 × 9.8 = 1960 Pa, so force down = 1960 × 0.010 = 19.6 N
pressure on bottom = 0.50 × 1000 × 9.8 = 4900 Pa, so force up = 4900 × 0.010 = 49.0 N
upthrust = 49.0 − 19.6 = 29.4 N

Answer: upthrust = 29.4 N upwards

Upthrust = weight of fluid displaced (Higher tier)

The cylinder above has a volume of 0.010 × 0.30 = 0.0030 m³. That volume of water has a mass of 0.0030 × 1000 = 3.0 kg and a weight of 3.0 × 9.8 = 29.4 N – exactly the upthrust. This is true for any shape:

upthrust = weight of fluid displaced

mass of fluid displaced = volume displaced × density of fluid; upthrust = mass displaced × g

Worked example: a stone under water

A stone of volume 400 cm³ is fully under water. Volume displaced = 400 cm³ = 4.0 × 10⁻⁴ m³
mass of water displaced = 4.0 × 10⁻⁴ × 1000 = 0.40 kg
upthrust = 0.40 × 9.8 = 3.92 N

Answer: about 3.9 N (in sea water, density 1030 kg/m³, it would be about 4.0 N)

Exam tip: Upthrust depends on the volume of fluid displaced and the density of the fluid – not on what the object is made of. Two objects of the same volume fully under water get the same upthrust.

Float or sink?

Compare the two forces on an object when it is fully immersed:

• upthrust > weight; What happens rises to the surface, then floats; Density compared with the fluid object less dense
• upthrust = weight; What happens stays where it is; Density compared with the fluid same density
• weight > upthrust; What happens sinks; Density compared with the fluid object more dense

A floating object settles at the depth where it displaces its own weight of fluid. So the less dense the object is compared with the liquid, the higher it floats.

Worked example: how much of a floating block is under water?

A wooden block of volume 1000 cm³ and mass 0.60 kg floats in water.
Floating, so upthrust = weight: it must displace 0.60 kg of water = 600 cm³
600 ÷ 1000 = 0.60, and the block’s density = 0.60 kg ÷ 0.0010 m³ = 600 kg/m³

Answer: 60% of the block is below the surface

Ships and loads

Steel is about eight times denser than water, yet steel ships float. The hull is hollow and full of air, so the average density of the ship is less than that of water and it can displace its own weight of water before the deck goes under.

• Adding cargo increases the weight, so the ship sinks lower, displaces more water and the upthrust increases until it equals the new weight.
• If it is overloaded, even the greatest possible upthrust (hull just under) is less than the weight, so it sinks.
• In denser sea water a ship floats a little higher than in fresh water, because a smaller volume gives the same weight of water displaced.

Common mistakes

• Saying “heavy things sink”. Whether something floats depends on its density compared with the fluid (or weight compared with upthrust), not on its weight alone.
• Thinking upthrust keeps increasing as a fully immersed object goes deeper. Once fully under, the volume displaced stays the same, so the upthrust does too.
• Writing that the upthrust always equals the weight. That is only true for a floating (or balanced) object.
• Using the volume of the whole object for a floating object. Only the part below the surface displaces fluid.
• Forgetting to convert cm³ to m³ (divide by 1 000 000) before using a density in kg/m³.

Revision questions

Try these, then check your answers below each one.

Question 1. What is upthrust? (Choose from: the upward force a fluid exerts on an object in it, the weight of an object when it is in water, the downward force of the water on the top of an object, the force needed to lift an object out of water.)

Answer: the upward force a fluid exerts on an object in it

Working: Upthrust is the upward force on an object that is partly or totally in a fluid (a liquid or a gas).

Question 2. An object hangs from a newton-meter. The reading is 5.0 N in air and 3.2 N when the object is fully under water.<br/>Calculate the upthrust on the object.

Answer: 1.8 N

Working: upthrust = 5.0 − 3.2 = 1.8 N.

Question 3. True or false? A steel ship floats because steel is less dense than water.

Answer: False

Working: False. Steel is about 8 times denser than water. The hollow hull contains air, so the average density of the ship is less than water and it displaces its own weight of water.

Related lessons

• Previous lesson: 11.3 Atmospheric Pressure
• Next lesson: 12.1 The Nature of Waves
• In this chapter: 11.1 Pressure and Surfaces
• In this chapter: 11.2 Pressure in a Liquid at Rest

Continue in the full course

This lesson is section 11.4 (AGCPH1104) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.