Chapter 13.3, Problem 35SSC

To determine

To Calculate: The density of cork.

Answer to Problem 35SSC

The cork is about $\frac{1}{10}$ as dense as water.

Explanation of Solution

Given data:

Cork floats with one-tenth of its volume below the water’s surface.

Formula used:

The increase of pressure with depth has an important consequence. It allows an individual to swim. That is, it creates an upward force, described as a buoyant force, on all objects. Every object in a liquid, even those that sink, has an apparent weight. This weight is less than when the object is in air.

One force is the upward force of the liquid on the object. There is also the downward force of the object’s weight. The difference between the buoyant force (or upward force) and the object’s weight whether an object floats or sinks.

The upward force or buoyant force can be calculated by using formula, $F_{buoyant}\text{ =}\rho Vg$ .

Where, V is the volume, $\rho$ is the density of fluid and g is the gravitational acceleration.

Calculation:

The weight of the water displaced equals the weight of the bobber.

So, $F_g\text{ =}{\rho }_{cork}{V}_{cork}g$

Therefore, $\frac{{\rho }_{cork}}{{\rho }_{water}}\text{ =}\frac{V_{water}}{V_{cork}}$

  $=\frac{1}{10}$

Conclusion:

The density about $\frac{1}{10}$ as water.