Question

When a polar bear on an iceberg notices that his 1870 N weight is just sufficient to sink the iceberg-?
WHAT IS THE WEIGHT OF THE ICEBERG?
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Answer 1

When a polar bear on an iceberg notices that his 1870 N weight is just sufficient to sink the iceberg-?

WHAT IS THE WEIGHT OF THE ICEBERG?

Solution:

Let:

$$P = 1870\,N$$ $$\rho(w) = 1000 \, \frac{kg}{m^3} - \text{density of water}$$ $$\rho(i) = 916.7 \, \frac{kg}{m^3} - \text{density of ice}$$

$m$-?

According to Archimedes’ principle:

$$P = \rho(w) g V - \rho(i) g V, \text{ were } V - \text{volume of iceberg}, \, g = 9.8\, \frac{m}{s^2}$$ $$P = V g (\rho(w) - \rho(i))$$ $$P = \frac{m}{\rho(i)} g (\rho(w) - \rho(i))$$ $$m = \frac{P \cdot \rho(i)}{g(\rho(w) - \rho(i)}$$ $$m = \frac{1870 + 916.7}{9.8 \cdot (1000 - 916.7)} = 2099.9 \, kg$$

Answer: 2099.9 kg.