State Archimedes' principle.

The upthrust on an object in a fluid equals the weight of fluid it displaces.

Write the equation for upthrust in terms of density.

U = ρVg, where ρ is the fluid density and V the volume of fluid displaced.

Why does a fluid exert an upthrust?

Pressure increases with depth, so the force on the lower surface of an object is greater than on the upper surface, giving a resultant upward force.

What is the condition for an object to float at rest?

Upthrust equals weight, so the resultant force is zero.

A fully submerged object has weight greater than the upthrust. What happens?

There is a downward resultant force, so it sinks.

A floating block has weight 4.7 N in water. What is the upthrust on it?

4.7 N, because it is in equilibrium.

What volume of fluid does a floating object displace?

Only the volume below the surface, enough for the weight of fluid displaced to equal the object's weight.

How does a submarine dive?

Ballast tanks are flooded, increasing its weight above the (fixed) upthrust.

What happens to the density of a sample when it is cut in half?

It is unchanged, as mass and volume both halve.

Density and upthrustEdexcel A-Level Physics: Flashcards

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Define density and give its SI unit.

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Define density and give its SI unit.: Density is mass per unit volume, ρ = m/V. Unit: kg m⁻³.
What is 1 g cm⁻³ in kg m⁻³?: 1000 kg m⁻³.
How do you convert a volume in cm³ to m³?: Multiply by 10⁻⁶.
State Archimedes' principle.: The upthrust on an object in a fluid equals the weight of fluid it displaces.
Write the equation for upthrust in terms of density.: U = ρVg, where ρ is the fluid density and V the volume of fluid displaced.
Why does a fluid exert an upthrust?: Pressure increases with depth, so the force on the lower surface of an object is greater than on the upper surface, giving a resultant upward force.
What is the condition for an object to float at rest?: Upthrust equals weight, so the resultant force is zero.
A fully submerged object has weight greater than the upthrust. What happens?: There is a downward resultant force, so it sinks.
A floating block has weight 4.7 N in water. What is the upthrust on it?: 4.7 N, because it is in equilibrium.
What volume of fluid does a floating object displace?: Only the volume below the surface, enough for the weight of fluid displaced to equal the object's weight.
How does a submarine dive?: Ballast tanks are flooded, increasing its weight above the (fixed) upthrust.
What happens to the density of a sample when it is cut in half?: It is unchanged, as mass and volume both halve.

Exam questions on Density and upthrust

A technician investigates a rectangular block of aluminium measuring 0.050 m × 0.040 m × 0.025 m. The block has a mass of 0.135 kg.
The block is cut into two equal halves. State what happens to the mass, volume and density of one half compared with the original block.2 marks
A wooden block of mass 0.48 kg and total volume 8.0 × 10⁻⁴ m³ is placed in fresh water of density 1000 kg m⁻³. It floats at rest. Take g = 9.81 N kg⁻¹.
Explain why the block floats with only part of its volume below the water surface.2 marks
A metal sphere is hung from a newtonmeter. In air the reading is 3.60 N. The sphere is then lowered until it is fully submerged in water of density 1000 kg m⁻³, without touching the container, and the reading falls to 2.25 N. Take g = 9.81 N kg⁻¹.
Calculate the volume of the sphere.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).