Question 14.6: A Titanic Surprise An iceberg floating in seawater as shown ...
A Titanic Surprise
An iceberg floating in seawater as shown in Figure 14.12a is extremely dangerous because most of the ice is below the surface. This hidden ice can damage a ship that is still a considerable distance from the visible ice. What fraction of the iceberg lies below the water level?
Conceptualize You are likely familiar with the phrase, “That’s only the tip of the iceberg.” The origin of this popular saying is that most of the volume of a floating iceberg is beneath the surface of the water (Fig. 14.12b).
Categorize This example corresponds to Case 2 because only part of the iceberg is underneath the water. It is also a simple substitution problem involving Equation 14.6.
\frac{V_{\text {disp }}}{V_{\text {obj }}}=\frac{\rho_{\text {obj }}}{\rho_{\text {fluid }}} (14.6)
Evaluate Equation 14.6 using the densities of ice and seawater (Table 14.1):
f=\frac{V_{\text {disp }}}{V_{\text {ice }}}=\frac{\rho_{\text {ice }}}{\rho_{\text {seawater }}}=\frac{917 kg / m^3}{1 030 kg / m^3}=0.890 \text { or } 89.0 \%Therefore, the visible fraction of ice above the water’s surface is about 11%. It is the unseen 89% below the water that represents the danger to a passing ship.
| Table 14.1 Densities of Some Common Substances at Standard Temperature (0°C) and Pressure (Atmospheric) |
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| Substance | ρ (kg/m³) | Substance | ρ (kg/m³) |
| Air | 1.29 | Iron | 7.86 × 10³ |
| Air (at 20°C and | Lead | 11.3 × 10³ | |
| atmospheric pressure) | 1.20 | Mercury | 13.6 × 10³ |
| Aluminum | 2.70 × 10³ | Nitrogen gas | 1.25 |
| Benzene | 0.879 × 10³ | Oak | 0.710 × 10³ |
| Brass | 8.4 × 10³ | Osmium | 22.6 × 10³ |
| Copper | 8.92 × 10³ | Oxygen gas | 1.43 |
| Ethyl alcohol | 0.806 × 10³ | Pine | 0.373× 10³ |
| Fresh water | 1.00 × 10³ | Platinum | 21.4 × 10³ |
| Glycerin | 1.26 × 10³ | Seawater | 1.03 × 10³ |
| Gold | 19.3 × 10³ | Silver | 10.5 × 10³ |
| Helium gas | 1.79 \times 10^{-1} | Tin | 7.30 × 10³ |
| Hydrogen gas | 8.99 \times 10^{-2} | Uranium | 19.1 × 10³ |
| Ice | 0.917 × 10³ | ||