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Fluids & Thermal Physics

Pressure & Buoyancy

One number decides sinking and floating, and neither the object's weight nor its depth is anywhere in it.

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Pressure & Buoyancy

One number decides sinking and floating, and neither the object's weight nor its depth is anywhere in it.

26 min3 checkpoints7 simulation tasks

Introduction

Sink or float

A steel ship floats. A steel bolt dropped over its side sinks: same metal, same ocean. So weight does not decide sinking and floating. One number does.

Predict

Two cubes of the same wood are lowered into water. One has twice the side length, so eight times the volume and the mass. What happens?

Try it

A wooden cube 0.20 m across floats 60.1% under. Shrink it to 0.12 m or less and drop it. Does it ride any higher?

GoalA wooden cube 0.12 m across or less, floating.

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What holds the block up

Everything about buoyancy comes from one fact: pressure in a fluid grows with depth. A depth hh below the surface, the fluid above is a column of weight ρfgh\rho_f g h per unit area, so

p(h)=patm+ρf g hp(h) = p_{\text{atm}} + \rho_f\, g\, h
Read the graph

Let the cube settle. How much bigger is the pressure on its bottom face than on its top face?

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kPa

Run the simulation first, then read the value off it.

Set the buoyant force equal to the weight, and a floating block rides with a fraction f=ρb/ρff = \rho_b/\rho_f of itself under. If ff comes out above one, it sinks: compare the densities.

Try it

Lead, at 11340 kg/m³, sinks in water. Choose a fluid that floats it.

GoalThe lead block floating.

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Depth does not enter into it

The dd that cancelled in the derivation is worth a second look.

Predict

An iron cube is released above the water and sinks to the tank floor. Sketch the buoyant force on it from release until it lands.

Loading the graph

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Practice

The iron block is fully submerged and still sinking. As it descends the rest of the way to the floor, what happens to the buoyant force on it?

Try it

If buoyancy does not change with depth, a cube can hover anywhere under the surface. Set the cube's density so it does.

GoalThe cube at rest in mid-water, off the floor and under the surface.

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Apparent weight

Read the graph

Drop the iron cube to the tank floor. How hard does the floor have to push up to hold it there?

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N

Run the simulation first, then read the value off it.

That number is the apparent weight, mg−FBmg - F_B: what a scale under the block would read. It is why a boulder you cannot budge on land can be rolled along a riverbed, and why you feel light in a swimming pool.

Predict

Set the tank fluid to air and drop the wooden cube. What do the readouts show once it is lying on the floor?

Try it

The tank now holds air. Make the buoyant force on the wooden cube as large as you can.

GoalA buoyant force above 0.16 N, in air.

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What comes next

You floated lead, hovered a cube in mid-water and measured buoyancy in air: the fluid pushed aside sets the force, and the object's weight and depth do not. Everything here was static, with pressure set by depth alone. Set the same fluid moving and the pressure starts to depend on how fast it is going.

Ideas this lesson took on

Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.

  • “Heavy objects sink and light ones float”
  • “The bigger block floats higher”
  • “The buoyant force grows as you go deeper”
  • “Air exerts no buoyant force”

Finished with this lesson?

Progress is stored on this device only. There is no account and nothing is sent anywhere.

Research behind this lesson

  • Heron et al. 2003: The companion paper: tutorials built directly on the documented difficulties, having students reason about the displaced fluid and the forces on it rather than be handed B = ρgV, proved effective, and K–8 teachers who worked through the same materials outperformed introductory physics students on some tasks.
  • Loverude et al. 2003: After standard instruction in hydrostatics, many science and engineering majors still could not predict or explain whether a simple object would sink or float. Some of the difficulties were specific to the buoyant force; many others traced back to ideas, mass, volume, density, the forces a fluid exerts, that instruction assumes are already secure before hydrostatics begins.
  • Loverude et al. 2010: Written questions and interviews found that many undergraduates never build a correct account of pressure in a static liquid: in particular they struggle to identify the forces acting on the liquid and to relate those forces to pressure.