How can the volume of an irregular solid be found?

By displacement: the rise in the water level of a measuring cylinder when the object is submerged.

The upward force on a body in a fluid, equal to the weight of fluid displaced.

Write the equation for upthrust.

U = ρfVg, with ρf the fluid density and V the volume of fluid displaced.

When does a body float?

When its upthrust equals its weight.

The viscous drag on a small sphere is F = 6πηrv.

State the conditions for Stokes' law to apply.

A small spherical object moving at low speed with laminar flow (no turbulence).

How does the viscosity of a liquid change with temperature?

It decreases as the temperature rises.

What is true of the forces on a sphere at terminal velocity?

The resultant force is zero: weight = upthrust + viscous drag.

Why are the timing marks placed well below the liquid surface in the falling-ball method?

So that the ball has reached terminal velocity before timing begins.

Why should the temperature be recorded in a viscosity experiment?

Viscosity depends on temperature, so the result only applies at that temperature.

Density, upthrust and viscous dragEdexcel International 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.: Mass per unit volume, ρ = m/V; kg m⁻³.
Convert 1 cm³ to m³.: 1 cm³ = 10⁻⁶ m³.
How can the volume of an irregular solid be found?: By displacement: the rise in the water level of a measuring cylinder when the object is submerged.
What is upthrust?: The upward force on a body in a fluid, equal to the weight of fluid displaced.
Write the equation for upthrust.: U = ρfVg, with ρf the fluid density and V the volume of fluid displaced.
When does a body float?: When its upthrust equals its weight.
State Stokes' law.: The viscous drag on a small sphere is F = 6πηrv.
State the conditions for Stokes' law to apply.: A small spherical object moving at low speed with laminar flow (no turbulence).
What is the unit of viscosity?: The pascal second, Pa s.
How does the viscosity of a liquid change with temperature?: It decreases as the temperature rises.
What is true of the forces on a sphere at terminal velocity?: The resultant force is zero: weight = upthrust + viscous drag.
What is the expression for η from a falling-ball experiment?: η = 2r²(ρs − ρl)g/(9v).
Why are the timing marks placed well below the liquid surface in the falling-ball method?: So that the ball has reached terminal velocity before timing begins.
Why should the temperature be recorded in a viscosity experiment?: Viscosity depends on temperature, so the result only applies at that temperature.

Exam questions on Density, upthrust and viscous drag

A student has a solid metal cube of side 2.0 cm. Its mass, measured on a balance, is 21.6 g.
The student has another solid object with an irregular shape that fits inside a measuring cylinder of water. Describe how the student could determine its density.2 marks
A solid cube of side 0.10 m and mass 0.80 kg is held fully submerged in water of density 1000 kg m⁻³. The acceleration of free fall is 9.81 m s⁻².
The cube is released from rest. Calculate the resultant force on it at the instant of release, and state its direction.2 marks
A steel ball bearing of radius 2.0 mm and density 7800 kg m⁻³ is released from rest at the surface of a tall tank of glycerol. The glycerol has density 1260 kg m⁻³ and viscosity 0.95 Pa s at the temperature of the experiment. The ball falls through the glycerol and reaches a constant terminal velocity. The acceleration of free fall is 9.81 m s⁻².
Calculate the weight of the ball and the upthrust on it when it is fully submerged.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).