IB Physics SL A 2 11 Buoyancy Questions

Practise IB Physics SL A.2.11 by explaining buoyancy and using force balance for floating or submerged objects.

Exam points

Explain buoyancy as the resultant pressure force from displaced fluid, including why pressure is greater at the lower surface.
Calculate buoyancy from fluid density, displaced volume and Fb = ρVg.
Use floating or submerged equilibrium to determine displaced volume, submerged fraction, object density or another force in the system.
Compare buoyancy with weight and other forces to justify floating, equilibrium, neglecting a small weight or motion from the bottom of a tank.
Predict how a change in fluid density, temperature, object density or displaced volume changes buoyancy or the floating condition.

Learn this topic

Study A.2.11—Buoyancy conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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 IB Physics SL A 2 11 Buoyancy Questions question 1 — IB Physics SL

(a)

Show that

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

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

[ 2 ]

Weight $=\rho_{c} \cdot A \cdot H \cdot g$

OR

Buoyancy $=\rho_{w} \cdot A \cdot D \cdot g$ $\rho_{c} \cdot A \cdot H \cdot g=\rho_{w} \cdot A \cdot D \cdot g$

<<algebraic manipulation to show the relationship>>

(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 $4200 \mathrm{~m}^{2}$ and height above sea level of 32 m .

The following data are available:

\begin{aligned} \rho_{\text {ice }} & =920 \mathrm{~kg} \mathrm{~m}^{-3} \\ \rho_{\text {seawater }} & =1030 \mathrm{~kg} \mathrm{~m}^{-3} \end{aligned}

[ 2 ]

(i)

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

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

[ 2 ]

$\begin{aligned} \text { «(H -32) /H = 920 / } 1030 \text { so } \text { » } \mathrm{H}=300 \text { 《m》 } \text { OR } \mathrm{D}=268 \text { "m" } \mathrm{m}=920 \times 300 \times 4200 \text { OR } 1.16 \times 10^{9} \text { "kg" } \end{aligned}$

Must see either full substitution or answer to 3 or more significant
figures.

All question bank results loaded

Learn this topic

IB Physics SL A 2 11 Buoyancy Questions question 1

Question (a)

Question (b)

Question (i)