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Den Hartog’s Mechanics

A web-based solutions manual for statics and dynamics

Problem 75

Let’s first decide on whether the ship goes up or down. Salt water is denser than fresh water, so it takes less salt water displacement to provide the buoyant force. Therefore, the ship should ride higher in salt water than in fresh.

The amount of freshwater displaced by the ship is

\frac{10,000 \cdot 2240}{62.4}

and the amount of saltwater displaced is

\frac{10,000 \cdot 2240}{1.02 \cdot 62.4}

The displacement difference is

\frac{10,000 \cdot 2240}{62.4} \left( 1 - \frac{1}{1.02} \right) = 7039\,\rm{ft^3}

With a cross-section of 12,000 square feet, the ship will ride

\frac{7039}{12,000} = 0.5866\,\rm{ft}

or about 7 inches higher in the salt water.

Problem 76Problem 74

Last modified: January 22, 2009 at 8:32 PM.