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16.8: Some Simple Examples

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    Aug 8, 2022
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As we pointed out in the introduction to this chapter, this chapter is less demanding than some of the others, and indeed it has been quite trivial so far. Just to show how easy the topic is, here are a few quick examples.

Example

A cylindrical vessel of cross-sectional area A is partially filled with water. A mass of ice floats on the surface. The density of water is and the density of ice is . Calculate the change in the level of the water when the ice melts, and state whether the water level rises or falls.

Example

A cork of mass , density , is held under water (density ) by a string. Calculate the tension in the string. Calculate the initial acceleration if the string is cut.

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Example

A lump of lead (mass , density ) is held hanging in water (density ) by two strings as shown. Calculate the tension in the strings.

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Example

A hydrometer (for our purposes a hydrometer is a wooden rod weighted at the bottom for stability when it floats vertically) floats in equilibrium to a depth in water of density . If salt is added to the water so that the new density is , what is the new depth ?

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Example

A mass , density , hangs in a fluid of density from the ceiling of an elevator (lift). The elevator accelerates upwards at a rate . Calculate the tension in the string.

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Example

A hydrometer of mass and cross-sectional area floats in equilibrium do a depth in a liquid of density . The hydrometer is then gently pushed down and released. Determine the period of oscillation.

Example

A rod of length and density ( ) floats in a liquid of density . One end of the rod is lifted up through a height so that a length remains immersed. I have drawn it with the rope vertical. Must it be?)

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i. Find as a function of .

ii. Find as a function of and .

iii. Find the tension in the rope as a function of and .

Draw the following graphs:

a. and versus .

b. versus for several .

c. versus for several .

d. versus for several .

e. versus for several .

Answers

1. No, it does not.

2.

3.

4.

5.

6.

7.

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This page titled 16.8: Some Simple Examples is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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    Jeremy Tatum
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