# Archimedes' Principle

Discussion in 'Jukwaa la Elimu (Education Forum)' started by MaxShimba, Nov 21, 2008.

1. ### MaxShimbaJF-Expert Member

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Archimedes' Principle says that the apparent weight of an object immersed in a liquid decreases by an amount equal to the weight of the volume of the liquid that it displaces. Since 1 mL of water has a mass almost exactly equal to 1g, if the object is immersed in water, the difference between the two masses (in grams) will equal (almost exactly) the volume (in mL) of the object weighed. Knowing the mass and the volume of an object allows us to calculate the density.

Discuss the principle.

2. ### MaxShimbaJF-Expert Member

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To determine the density of an object by two different methods and to compare the results.

3. ### MaxShimbaJF-Expert Member

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The object you have is a cube of metal. The volume of a cube can be found from the formula V=a3, where a is the length of one edge in centimeters. The mass of the cube can be found by weighing it. Then the density can be determined by dividing the mass by the volume.

4. ### MaxShimbaJF-Expert Member

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Tradition tells us that the king was suspicious about the purity of the gold in his crown and asked Archimedes to find a way to determine if it was the real thing. Solving the problem seemed to be impossible because in those days (3rd century B.C.) nothing was known about chemical analysis. One day Archimedes was thinking about the problem while taking a bath. As he lay floating in the bathtub he thought about his "weightless" body. Suddenly he realized that all bodies "lose" a little weight when placed in water, and the bigger their volume, the more weight they lose. He realized that the density of a metal can be found from its weight and its weight loss in water. The weight of the King's crown and its apparent loss of weight in water would tell him if it were made out of pure gold. Archimedes shouted "Eureka!" (I have found it!) and rushed out into the street naked to announce that he had solved the problem. Today the effect he observed is called Archimedes' Principle.

5. ### OpaqueJF-Expert Member

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Is mL the correct dimension of volume?

6. ### MaxShimbaJF-Expert Member

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The size of the body that is immersed is equal to the amount of liquid that is lost from the bathtab/bow which will be the volume of the body in liters/gallons etc..

7. ### MshiiriJF-Expert Member

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Yeah
ml, cl dl, l, etc

#8
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Statement:

When a body is partially or totally immersed in a fluid it experiences an upward force which is equal to the weight of fluid displaces.

Units
The SI unit of volume is cubic meter (s).

9. ### MaxShimbaJF-Expert Member

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Procedure

Method 1: Determination of density by direct measurement of volume.

The object you have is a cube of metal. The volume of a cube can be found from the formula V=a3, where a is the length of one edge in centimeters. The mass of the cube can be found by weighing it. Then the density can be determined by dividing the mass by the volume.

a. Weigh your cube on the electronic scale. Record your mass below.

b. Measure the edge of the cube in centimeters with your plastic ruler. Record the length below.

b. Calculate the volume. Record the volume below.

d. Calculate the density. Record the density below.

DATA

Mass of object: m1 = ______________ g

Length of edge of object = _____________ centimeters

Volume of object: V = edge x edge x edge = ______________ cubic centimeters (cc)

D = mass/volume = ____________ grams per cubic centimeter (cc)

(mass divided by volume)

10. ### MaxShimbaJF-Expert Member

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Nov 23, 2008
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Method 2: Archimedes' Principle

Archimedes' Principle says that the apparent weight of an object immersed in a liquid decreases by an amount equal to the weight of the volume of the liquid that it displaces. Since 1 mL of water has a mass almost exactly equal to 1g, if the object is immersed in water, the difference between the two masses (in grams) will equal (almost exactly) the volume (in mL) of the object weighed. Knowing the mass and the volume of an object allows us to calculate the density.

a. Record m1 below from the value on the previous page.

b. Set up balance arm hooked to wooden block and paper clip on other end.

c. Hang your cube on the paper clip.

d. Read the mass on the scale. This is m2. Don't worry if it is different from m1.

e. Fill the beaker with water up to within one inch of the top rim.

f. Immerse your cube in the water, being careful not to let it touch the walls or bottom.

g. Read the mass on the scale. This is m3. Record m3 below.

h. Subtract m2 from m3 and record the difference.

i. Calculate the density: divide m1 by the difference m2 - m3.

DATA

Mass of your object (m1 from the previous page): m1 = ______________ g

Electronic scale reading with object hanging on balance arm in the air: m2 = __________ g

Electronic scale reading with object on balance arm immersed in water: m3 = __________ g

Difference in mass of your object: m2 - m3 = _____________ g

m1

D = ---------- ________________ grams per cc

m2 - m3

Questions:

1. How do the two densities compare?

2. Why is Archimedes' Principle so important and well remembered if there is another perfectly good way (method 1) of measuring density?

Materials Required

5 Electronic lab scales (capacity 1200 g, ±0.1g)

5 250 mL beakers

30 metal objects -- all cubes, including lead!!

30 plastic metric rulers

5 wooden meter sticks

5 metal fulcrums

10 metal hangers

5 laboratory electronic calculators, placed in on benches as follows from left to right: 1,1,2,2

Box of regular size paper clips

5 special wooden blocks with hooks to be placed on electronic balances as counter weights.

11. ### MaxShimbaJF-Expert Member

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Yap, it is.

12. ### MaxShimbaJF-Expert Member

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For an object more dense than water

SG = (WS / V) / (WW / V) = WS / WW = WS / (buoyant force) = WS / (loss of weight in water)
= WS / (WS - weight of substance in water)

This suggests a method for determining the SG of an object more dense than water; namely, weight an object in air and weigh it while completely immersed in water. The SG would then be the weight in air divided by the apparent loss of weight when weighed in water.

A device called a Jolly Balance is designed to measure the weight of objects in air and in water by reading the elongation of a spring. It utilizes a Vernier scale to read the elongation of the spring to the nearest 0.1 mm, and so is very precise. Hooke's law

F = - k x
should apply to the spring, where F is the force (weight) that stretches the spring by an amount x, and k is the spring constant. Substituting into the equation above, we find

SG = WS / (WS - weight of substance in water) = (k xA) / (k xA - k xW)
When the unknown spring constant is canceled, the SG may be found using only the two spring elongations

xA: the object in air
xW: the object completely submerged in water

SG = xA / ( xA - xW)

13. ### MaxShimbaJF-Expert Member

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For an object less dense than water

The equation above is only true if the object is more dense than water. If the object is less dense than water, a lead weight must be attached and three spring elongations must be measured to determine the SG. The three elongations are

xA: the object alone, in air
xB: the object in air with the lead sinker submerged completed in water
xC: both the object and the sinker completely submerged in water
The latter two elongations are used to determine the loss of weight in water, that is, the denominator of the SG definition. You should derive this formula in terms of xA, xB, and xC.
SG = WS / (loss of weight in water) = ?

Having determined the SG for sinking and floating objects using Archimedes' Principle and the Jolly Balance, it is desirable to use an independent method for comparison. Since SG = S / W, and since W = 1 gram/cm3), one can determine the density of the object by measuring its mass and volume directly.

For a liquid
The Volumetric Flask (or Pycnometer) has a hollow stem stopper that allows one to prepare equal volumes of fluids very reproducibly. If the mass of the flask is measured (1) when empty, (2) when filled with the fluid, and (3)when filled with water, the SG of the fluid can be determined. Since the volume is the same, it will cancel out of the SG fraction.

14. ### OpaqueJF-Expert Member

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Ok, nilikuwa namaanisha volume dimensions katika density ya water, is it gram/mL OR gram/cc? Baadaye nikaja kukumbuka that the volume of 1mL=1cc, so the man was right opting to use mL. Thanks, tuendelee kujadili .....

15. ### KijakaziJF-Expert Member

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Baadaye ukaja kukumbula!!!! haupaswi kukumbuka kitu kama hicho unapaswa kujua.. yaani hata ukiamshwa usingizini unapaswa ujue vinginevyo yapo masomo mengi ambayo mtu hapaswi kuwa na uelewo mkubwa!

16. ### MaxShimbaJF-Expert Member

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1. State Archimedes' Principle.

2. What is specific gravity?

3. Why are you advised to make several measurements of the diameter of the ball, not all in the same plane? (Besides obviously reducing the random error.)

4. Why should alcohol be used in the pycnometer before the water?

5. The density of pure isopropyl alcohol is 0.810 gram/cm3. The alcohol used in this experiment was 30% water (by volume). What calculation was made to find the new density? Show that this gives the answer for 70% isopropyl alcohol found in the lab writeup.

6. What is the formula for determining the specific gravity of the floating ball in terms of the three measured elongations? (Hint: it is NOT the same as equation (3) for the sinking ball.)

7. A glass of water contains a large piece of ice floating without touching the bottom of the glass. As you know, some of the ice extends above the surface of the water. As the ice melts, will the level of water in the glass rise, remain the same, or fall? Explain.

17. ### MaxShimbaJF-Expert Member

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Procedure
You must perform three separate experiments in which you will determine the density and specific gravity of

1. a solid more dense than water
2. a solid less dense than water
3. a liquid

Set up the Jolly Balance
Level the Jolly balance using the screws on the legs so that the scribed rod does not touch the clear plastic sleeve.

Set the Vernier scale to zero (0.00 cm) using the knob near the base.
Move the clear plastic sleeve until the scribe line on it is aligned with the scribe line on the hanging metal rod.

The Jolly balance is now calibrated to read zero when there is no load on the spring, so the clear plastic sleeve MUST NOT BE MOVED for the duration of the experiment.

18. D

### DarwinJF-Expert Member

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http://www.jamiiforums.com/jukwaa-la-elimu-education-forum/20296-church-apologizes-darwin.html

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Default Re: Church apologizes to Darwin!!

next thing you know the Church will hijack evolution, and claim the account in genesis is not literal, and that it is in need of a more current interpretation, and that the lord works in mysterious way.

I tell you if you think Quantum Physics was confusing, try organized religion.

19. ### MaxShimbaJF-Expert Member

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Naona jamaa amepagawa na kufikiria hapa ni mahala pa kusoma uchafu na upumbavu wa darwin.

Kama huna hoja kuhusu Archimedes, kaa kimya. Hiki si kijiwe cha walio changanyikiwa akili.

20. D

### DarwinJF-Expert Member

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