Question

When a polar bear jumps on an iceberg, he notices that his 420 lb weight is just sufficient to sink the iceberg. What is the weight of the iceberg? Density of salt water is 64 lb/ft³ and that of iceberg is 57.2 lb/ft³.

Answer 1

Question #85047 — Physics — Molecular Physics | Thermodynamics

When a polar bear jumps on an iceberg, he notices that his 420 lb weight is just sufficient to sink the iceberg. What is the weight of the iceberg? Density of salt water is $64\mathrm{lb / ft^3}$ and that of iceberg is $57.2\mathrm{lb / ft^3}$.

Solution

Let us introduce next notations

$V_{i}$ -volume of the iceberg, $\rho_{i}$ -density of the iceberg, $\rho_{w}$ -density of the water,

$m_{b}$ - mass of the bear, g- is the acceleration due to gravity, Archimedes force: $F_{A}$ and force of gravity $F_{g}$, where $\rho_{i}V_{i}$ -is the mass of iceberg.

In our system we have only two forces $F_{A}$ and $F_{g}$ witch joined by condition of equilibrium

$$F _ {A} = F _ {g},$$

From the Archimedes law we obtain $F_{A} = \rho_{W} g V_{i}$, and the resulting force of gravity for bear and iceberg: $F_{g} = (\rho_{i} V_{i} + m_{b}) g$.

Now from (1)

$$\rho_ {W} g V _ {i} = \left(\rho_ {i} V _ {i} + m _ {b}\right) g \Rightarrow V _ {i} = \frac {m _ {b}}{\rho_ {w} - \rho_ {i}}$$

So the mass of iceberg

$$m _ {i} = V _ {i} = \rho_ {i} \frac {m _ {b}}{\rho_ {w} - \rho_ {i}} = 57.2 \left[ \mathrm{lb/ft^3} \right] \frac {420 [ \mathrm{lb} ]}{64 \left[ \mathrm{lb/ft^3} \right] - 57.2 \left[ \mathrm{lb/ft^3} \right]} = 3532.94 [ \mathrm{lb} ]$$

Answer: weight of the iceberg 3532.94 lb

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