College Physics
OER 2016 Edition
ISBN: 9781947172173
Author: OpenStax
Publisher: OpenStax College
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Chapter 11, Problem 3TP
To determine
(a)
The density of polystyrene cube if 90% floats above the surface of water.
Expert Solution
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:
Substitute
for 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.
Expert Solution
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 m
for 
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.
Expert Solution
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 is
The density of polystyrene block is
Therefore, the block can remain partially submerged in ethyl alcohol.
Substitute
for 
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.
Expert Solution
Explanation of Solution
When the material is a spherical, the following steps can be used to find out the density.
- The mass of the material should be found.
- Use the thread to wrap the sphere for finding the circumference of the sphere.
- The radius can be calculated from the circumference
- The volume is calculated from the radius
- 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.
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Students have asked these similar questions
Exercise 1:
(a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre-
sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case
j = 1.
(b) Verify that they satisfy the so(3) Lie algebra commutation relation:
[D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h).
(c) Prove the identity
3
Dm'm,(β) = Σ (D(Ρ)D(Ρ))m'¡m; ·
i=1
Sketch the harmonic.
For number 11 please sketch the harmonic on graphing paper.
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