IB Physics SL A.2.11 Buoyancy

Practise calculating buoyancy from displaced-fluid volume and density, then balancing it with weight or spring force for floating, submerged and accelerating objects.

Syllabus
First assessment 2025
Objective
—
Level
SL

Exam points

  • calculate buoyancy as ρfluidVdisplacedg rather than using the object's density or total volume blindly
  • set buoyancy equal to weight for floating equilibrium and derive the submerged fraction from densities
  • combine buoyancy with weight, drag or spring force using signed vertical force balance

A.2.11—Buoyancy question 1

[Maximum number: 4]

A cylindrical cork of height H and cross-sectional area A is floating stationary in water. Its depth below the water surface is D.

Figure for Question A.2.11—Buoyancy question 1 — IB Physics SL

Question (a)

(a)

Show that

DH=ρcρw\frac{D}{H}=\frac{\rho_{\mathrm{c}}}{\rho_{\mathrm{w}}}

where ρc\rho_{\mathrm{c}} is the density of the cork and ρw\rho_{\mathrm{w}} is the density of water.

[ 2 ]

Question (b)

(b)

An icebreaking ship is designed to withstand a collision with an iceberg, a large partially submerged body of ice freely floating in water. The designers model the shape of the iceberg as a cylinder with an approximate cross-sectional area of 4200 m24200 \mathrm{~m}^{2} and height above sea level of 32 m .

The following data are available:

ρice =920 kg m−3ρseawater =1030 kg m−3\begin{aligned} \rho_{\text {ice }} & =920 \mathrm{~kg} \mathrm{~m}^{-3} \\ \rho_{\text {seawater }} & =1030 \mathrm{~kg} \mathrm{~m}^{-3} \end{aligned}
[ 2 ]

Question (i)

(i)

Show that the mass of the iceberg is about 1.2×109 kg1.2 \times 10^{9} \mathrm{~kg}.

The designers assume that the mass of the ship is about 140\frac{1}{40} the mass of the iceberg and is moving at 12 m s−112 \mathrm{~m} \mathrm{~s}^{-1} when it collides with the iceberg. They stick together after the collision.

[ 2 ]
All question bank results loaded