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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 6, Problem 4P

(a)

To determine

**To show that:** The percentage of the volume of the object above the surface of the liquid is

Expert Solution

**Given information:**

The buoyant force is

The weight of the object is

**Calculation:**

Consider the volume above the surface as follows:

Modify Equation (1).

Divide both sides of the Equation by

Apply Archimedes Principle as shown below.

Substitute *F* and *W* in the above Equation.

Substitute

Find the percentage of the volume above the surface.

Therefore, the percentage of the volume of the object above the surface of the liquid is

(b)

To determine

**To calculate:** The percentage of the volume of an iceberg above the water.

Expert Solution

The percentage of the volume of an iceberg above the water is

**Given information:**

The density of ice is

The density of seawater is

**Calculation:**

Refer to part (a).

The percentage of the volume of the object above the surface of the liquid is

Substitute

Therefore, the percentage of the volume of an iceberg above the water is

(c)

To determine

**To show:** Does the water overflow when the ice melts?

Expert Solution

The water does not overflow when the ice melts.

**Given information:**

An ice cube floats in a glass filled to the brim with water.

**Calculation:**

Let

Refer to part (a).

The volume of ice above the surface of the water is

The volume below the surface of the water is,

Suppose the mass of the ice cube is the same as the mass of the water which is formed when the cube melts.

So, when the ice cube melts the volume of the resulting water is same as the underwater volume of the ice cube.

Hence, the water does not overflow when the ice melts.

(d)

To determine

**To calculate:** The work required to completely submerge the sphere.

Expert Solution

The work required to completely submerge the sphere is

**Given information:**

A sphere of radius 0.4 m.

Density of the water is

**Calculation:**

Suppose the height of the exposed part of the ball is *y*.

Sketch the instant when the height of the exposed part of the ball is *y* as shown in Figure 1.

Refer to Figure 1.

Find the volume of the segment of a sphere as shown below.

Substitute 0.4 m for *r* and *h* in Equation (3).

Modify the above Equation as shown below.

Find the work done to submerge the sphere.

Therefore, the work required to completely submerge the sphere is