Example 5.6 from College Physics, 5.3 Elasticity: Stress and Strain

Calculating Change in Volume with Deformation: How Much Is Water Compressed at Great Ocean Depths?

Calculate the fractional decrease in volume ( $\frac{Δ V}{V_{0}}$ ) for seawater at 5.00 km depth, where the force per unit area is $5 . 00 \times 10^{7} N / m^{2}$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Equation $Δ V = \frac{1}{B} \frac{F}{A} V_{0}$ is the correct physical relationship. All quantities in the equation except $\frac{Δ V}{V_{0}}$ are known.
Solution
Solving for the unknown $\frac{Δ V}{V_{0}}$ gives
$\frac{Δ V}{V_{0}} = \frac{1}{B} \frac{F}{A} .$
5.46

Substituting known values with the value for the bulk modulus $B$ from Table 5.3,
$\begin{array}{l} \frac{Δ V}{V_{0}} & = & \frac{5.00 \times 10^{7} {N/m}^{2}}{2 . 2 \times 10^{9} {N/m}^{2}} \\ = & 0.023 = 2.3%. \end{array}$
5.47
Discussion
Although measurable, this is not a significant decrease in volume considering that the force per unit area is about 500 atmospheres (1 million pounds per square foot). Liquids and solids are extraordinarily difficult to compress.

0 of 3 steps open

How did it go?

Strategy

Solution

Discussion

Strategy

Solution

Discussion