Chapter 11, Problem 3TP

To determine

(a)

The density of polystyrene cube if 90% floats above the surface of water.

Answer to Problem 3TP

The density of polystyrene cube if 90% floats above the surface is

Explanation of Solution

Given:

Density of water,

Volume of liquid,

Formula Used:

A polystyrene cube floating partially immersed in a container is considered. The relation between the density and volume of liquid and of object is given as,

Calculation:

Substitutefor V and for

Conclusion:

Therefore, the density of polystyrene cube if 90% floats above the surface is

To determine

(b)

The percentage of volume that remains outside of water.

Answer to Problem 3TP

The percentage of volume remaining outside of water is 40%.

Explanation of Solution

Given:

Given:

Density of water,

Volume of liquid,

Mass,

Formula:

If the mass is located on polystyrene block, the total weight acting downwards will increases which causes the block to immerse still more.

Hence the equation becomes,

Where mass which placed over the block.

For solving, the equation can be rearranged,

Calculation:

Substitute for for 0.5 kg for mfor

Thus, the percentage of volume remaining outside of water is 40%.

Conclusion:

Therefore, the percentage of volume remains outside of water is 40%.

To determine

(c)

Whether or not, the block can remain partially submerged in the new fluid.

Whether or not, the block can remain partially submerged in ethyl alcohol with 0.5 kg mass placed on top.

Answer to Problem 3TP

Yes, the block can remain partially submerged in ethyl alcohol.

Yes, the block can remain 76% submerged in ethyl alcohol with mass placed on top.

Explanation of Solution

Given:

Density,

Volume of liquid, Volume of liquid,

Mass,

Formula Used:

The volume of block immersed in alcohol with a mass is placed over the block is given as,

Calculation:

The object floats when its density is lesser than that of the fluid density. The density of ethyl alcohol isThe density of polystyrene block isTherefore, the block can remain partially submerged in ethyl alcohol.

Substitutefor for for m for

The volume fraction could be

Conclusion:

Therefore, the block can remain partially submerged in ethyl alcohol. The block can remain 76% submerged in ethyl alcohol with mass placed on top.

To determine

(d)

The way the density of polystyrene can be determined.

Explanation of Solution

When the material is a spherical, the following steps can be used to find out the density.

1. The mass of the material should be found.
2. Use the thread to wrap the sphere for finding the circumference of the sphere.
3. The radius can be calculated from the circumference
4. The volume is calculated from the radius
5. The density of the material is found by using mass and radius by using the following equation

Conclusion:

Therefore,the density of polystyrene is determined without the water container by using spherical material by finding the radius and circumference of the sphere and the mass of the material.