Density and upthrust Cambridge International AS & A Level Physics revision
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In plain words
Things feel lighter in water because the water pushes up on them. The rule is surprisingly simple: the push equals the weight of the water the object shoves out of the way. If that is as much as the object's own weight, it floats.
Three things to know
- Density ρ = m ÷ V, in kg/m³. Water has a density of 1000 kg/m³.
- Upthrust = weight of fluid displaced = ρVg, where ρ is the density of the fluid and V is the volume of the object that is below the surface (Archimedes' principle).
- A floating object displaces its own weight of fluid. An object denser than the fluid sinks, because even fully submerged the upthrust is less than its weight.
Worked example
A block of volume 2.0 × 10⁻⁴ m³ and weight 5.0 N is held fully under water. Find the upthrust, and say what happens when it is let go.
- Upthrust = ρVg = 1000 × 2.0 × 10⁻⁴ × 9.81 = 1.96 N.
- The weight (5.0 N) is bigger than the upthrust (1.96 N).
- The resultant force is downwards, so the block sinks.
Tips and tricks
- In ρVg use the density of the fluid, not the density of the object.
- 1 g/cm³ = 1000 kg/m³, and 1 cm³ = 1 × 10⁻⁶ m³.
It lands in your notebook with its questions as flashcards.
Density and upthrust: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the upthrust on an object equal to?
This is Archimedes' principle.
What is the density of an object of mass 600 g and volume 200 cm³?
600 ÷ 200. That is 3000 kg/m³.
An object floats at rest in a liquid. How does the upthrust on it compare with its weight?
It is in equilibrium.
An object is fully submerged in water, and then in a denser liquid. What happens to the upthrust on it?
The same volume of a denser fluid weighs more.
An object sinks in water. What does that tell you?
Even fully submerged, it displaces less than its own weight of water.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
Density and upthrust
Cambridge International AS & A Level Physics 9702 · 7 marks · papermunch.org
Name ______________________________ Date ______________
A block has a mass of 2.7 kg and a volume of 1.0 × 10⁻³ m³. Find its density.[2]
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2700 kg/m³.
Find the upthrust on an object of volume 5.0 × 10⁻⁴ m³ fully submerged in oil of density 900 kg/m³.[2]
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4.4 N. 900 × 5.0 × 10⁻⁴ × 9.81.
A boat of mass 1200 kg floats in fresh water of density 1000 kg/m³. Find the volume of water it displaces.[3]
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1.2 m³. A floating object displaces its own weight of water, so it displaces 1200 kg of water.
Answers: Density and upthrust
- 1. 2700 kg/m³.
- 2. 4.4 N. 900 × 5.0 × 10⁻⁴ × 9.81.
- 3. 1.2 m³. A floating object displaces its own weight of water, so it displaces 1200 kg of water.