An object falls off of a pier and into Lake Michigan (pure water) where it displ

Question

An object falls off of a pier and into Lake Michigan (pure water) where it displaces a total volume of 56.5 cubic feet of water. What is the buoyant force acting on the object in newtons? You will need to convert units in order to answer the problem in Newtons.

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Table 4.4 Densities of Some Common Substances Mass Density, Weight Density, Specific Substance Type D (kg/m Dw (lb/fi Gravity Solids Styrofoam. 37 2.3 0.037 Juniper wood 560 35 0.56 Ice 57.2 0.917 Ebony wood ,200 1.2 Concrete 2,500 56 2.5 Aluminum 2,700 68 2.7 Granite 2,700 68 2.7 Diamond 3,400 210 3.4 7,860 Iron 490 7.86 Brass 8,500 530 8.5 Nickel 8,900 555 8.9 Copper 8,930 557 8.93 Silver 655 10.5 10,500 11,340 Lead 11.34 708 Uranium 9,000 1,190 Gold 9,300 1,200 9.3 Liquids Gasoline 680 42 0.68 Ethyl alcohol 79 49 0.79 Water (pure) 1,000 62.4 1.00 Seawater 030 64.3 1.03 Antifreeze 1,100 67 1.1 Sulfuric acid 830 14 1.83 Mercury 3,600 849 3.6 Gases (at 0°C and 1 atm) Hydrogen 0.09 0.0056 0.00009 Helium 0.18 0.011 0.00018 Air 1.29 0.08 0.00129 Carbon dioxide 0.00198 1.98 0.12 Radon 10 0.627 0.010 Note: "e' stands for element, "c" for compound, and "m" for mixture.

Explanation / Answer

Given Data

Volume displaced by the object , V = 56.5 ft3

Volume, V = 56.5 * 0.0283168= 1.599 m3              

(Since 1 ft3 = 0.0283168 m3 )

The buyoyant force acting on the object , F = V * Density of water * g

                                                            F = 1.599* 9.81* 1000

                                                            F = 15695 .01 N

The buoyant force acting on the object in newtons is = 15695.01 N = 1.5695 * 104 N

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