phy11l a4 e206

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E206: ARCHIMEDES’ PRINCIPLE

FRISNEDI, Nadine T.

OBJECTIVE

This experiment has four parts in which there are

two main objectives that must be achieved. He

first one is to study Archimedes’ principle.

Archimedes’ Principle states that the upward force

which is the buoyant force that is exerted on a

body partially or fully immersed in liquid is equal

to weight of the liquid that the body displaces. The

purpose of this experiment is to showcase the

science behind Archimedes’ principle,

determination of the density and specific gravity

of unknown solid and liquid model through their

weight loss with the help of Archimedes’ principle

and the experiment.

The second objective is to apply Archimedes’

principle in determining the density and specific

gravity of solids and liquids. Density is the physical

property of a substance which is the ratio of mass

to volume while specific gravity is dimensionless

but it is the ratio of the density of a substance to

the density of a reference substance. Water is

commonly used as the reference substance.

This experiment will help students to understand

how density is related to Archimedes’ principle and

be able to gain more knowledge and appreciation

about the concepts in density and specific gravity.

The students will also know how the weight of an

object affects its density.

At the end of the experiment, it is expected for the

students to learn Archimedes’ Principle and

understand the presence of an upward force when

an object is immersed in a liquid.

The significance of this experiment is that it is a

way of showing why and how some objects sink

while others do not and also help the students be

able to understand the applications of the given

laboratory formulas in solving problems involving

Physics.

Equipment used should be handled with care and

procedures must be followed correctly to avoid the

occurrence of problems.

MATERIALS AND METHODS

Since the equipment used in this experiment

requires proper care, the best strategy of our

group was to follow the procedures and conduct

the experiment properly. It is also necessary that

to make sure that the samples won’t be

contaminated. Electronic balance, hydrometer,

two pieces if 250-ml graduated cylinder which

contains water and denatured alcohol, three

pieces of 250-ml beaker, cork, string and 2 pieces

of metal specimen were the materials and

equipment used in the experiment. (See Figure 1).

Figure 1. Materials and equipment used in the experiment.

To be able to use time efficiently, the students

were instructed to label the two graduated

cylinders with sample 1 and 2. It was revealed that

the clear one was water and was labeled as sample

1 while the yellowish liquid is actually denatured

alcohol and labeled as sample 2. A hydrometer

was used in this part since it can measure the

specific gravity or relative density of the two

liquids which are the denatured alcohol and water.

This part is actually the third part of the

experiment, it would be time consuming to

transfer the liquids more than once so the students

performed the third part of the experiment first.

Another thing about the hydrometer is that it is

made of fragile glass and it needs an extra care

before using because of sensitivity. The

hydrometer was submerged downward on the first

sample until its tip will touch the bottom part of

the graduated cylinder and was released and

allowed to float. The specific gravity was

determined by the reading on the hydrometer. A

photo was taken in order to have an accurate

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measurement of the specific gravity of the liquid

sample. To make sure that the other liquid sample

won’t be contaminated, the hydrometer was wiped

dry. The same procedure was done for the second

liquid sample.

Figure 2. Determining the Specific Gravity of Liquid Sample 2

The experimental values of each sample were

compared to the actual values which are given in

the table and the percent error was computed for

both samples.

After doing the third part, the group then focused

on the first part of the experiment which deals with

the determination of the specific gravity of an

unknown solid sample that is heavier than water.

The group decided that the metal specimen which

is gray in color as the sample 1. The string

connected on it was tied loosely in such way that

it can hang on the hook under the suspended

electronic balance. The electronic balance was set

to grams and made sure that the reading is in zero

before putting the metal sample. The reading from

the electronic balance was recorded as weight in

air, 𝑊𝐴.

Figure 3. Getting the Weight in air of Metal Sample 1

The students were instructed to use another

beaker to be filled with tap water from the faucet.

Afterwards, the sample was submerge completely

in a beaker of tap water but remember to not let

it touch the bottom of the beaker and measure its weight while it is in water, 𝑊𝑊.

Figure 4. Getting the Weight in water of Metal Sample 1

The students then computed for the loss of weight

of the sample was computed by getting the

difference of the weight of the metal sample in the

electronic balance and its weight while submerged

in water. Then, the specific gravity of the metal sample was determined using the equation: 𝑆𝐺 =

𝑊𝐴

𝑊𝐴−𝑊𝑊. The same procedures were repeated using

the other sample (the gold one).

Figure 5. Getting the Weight in air of Metal Sample 2

Figure 6. Getting the Weight in water of Metal Sample 2

It was identified that Sample 1 was aluminum and

Sample 2 was brass since computed specific

gravity that for both samples are closest to those

types of metals based from the table of densities

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of some solids and liquids. The experimental

values of both samples were compared with the

actual values to get the percent error.

The second part of the experiment deals with the

determination of the specific gravity of unknown

liquid samples. The students choose the aluminum

as the metal sample to be used. Since the weight

in air and weight in water of aluminum has already

been measured, we can use the data already. The

liquid samples were transferred into their assigned

beakers and labeled as sample 1 and 2.

Figure 7. Transferring the Liquid Sample 1 to the beaker.

Figure 8. Transferring the Liquid Sample 2 to the beaker.

After getting the weight in air and in water, the

aluminum metal was submerged completely into

sample 1 but remember to not let it touch the

bottom of the beaker and recorded its weight in the liquid, 𝑊𝐿.

Figure 9. Getting the Weight in liquid of aluminum in Sample 1

Again, we find the loss of weight of body in liquid

by getting the difference of the weight of the

aluminum in the electronic balance and its weight

while submerged in the liquid. The specific gravity

of the liquid was computed using the

equation: 𝑆𝐺 =𝑊𝐴−𝑊𝐿

𝑊𝐴−𝑊𝑊 . Using a different liquid

sample, the procedures were repeated. After

gathering all the data, the experimental values of

the densities of the liquids were computed and

then compared to its actual values based from the

given tabulation of densities of some solids and

liquids in the laboratory manual so it can be

identified. The percent error for both liquids were

computed.

For the last part of the experiment, which is the

determination of specific gravity of a solid lighter

than water. The cork was the main material to be

observed. The group decided to ask for an

additional piece of string from the laboratory

assistants in order to get the weight of the cork by

tying the cork to the string and attaching it to the

hook under the electronic balance.

Figure 10. Getting the Weight in air of cork

The metal sample that we used was the brass

which served as the sinker. The string was

attached to the cork and the sinker hung below it.

The sinker was submerged to the water while the

cork was attached above it. The weight of the cork

while the sinker was submerged was recorded as 𝑊𝐶𝐴−𝑆𝑊.

Figure 11. Getting the Weight of cork in air and sinker in water.

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Next, both the sinker and the cork were

submerged to the water and their weight was

recorded as 𝑊(𝐶+𝑆)𝑊. The loss of weight of the cork

was computed by getting the difference of the

weight of cork while the sinker was submerged

and the weight when both the cork and the sinker

is submerged into the water. The specific gravity

of the cork was computed by using the equation:

𝑆𝐺 =𝑊𝐴

𝑊𝐶𝐴−𝑆𝑤−𝑊(𝐶+𝑆)𝑤.

OBSERVATIONS AND RESULTS

In the first table, the weight of the brass and the

aluminum was obtained using the electronic

balance. Their weight in water was also obtained

when they have been submerged into water while

the string is attached to the electronic balance.

The specific gravity was determined using the

weights of two unknown metal samples in air and

their weight in water. The specific gravity was

computed using the equation: 𝑆𝐺 =𝑊𝐴

𝑊𝐴−𝑊𝑊 .

Observing the data gathered from Table A, it

shows that the first and second metal has a

specific gravity of 2.7257 and 8.1333,

respectively. From the comparison of the specific

gravity of known objects, the two sample metals

are aluminum and brass. The percent error we

have computed were 0.9505% for aluminum and

3.6335% for Brass.

TABLE A. Determining the Specific Gravity of

an Unknown Solid Sample Heavier

Sample 1 Sample 2

weight in air, 𝑊𝐴 30.8 g 48.8g

weight in water, 𝑊𝑤 19.5g 42.8g

Specific Gravity,

𝑆𝐺 =𝑊𝐴

𝑊𝐴 − 𝑊𝑊

2.7257 8.1333

Name of Sample Aluminum Brass

Percent Error 0.9505% 3.6335%

Sample Computation for Sample 1

Given: 𝑊𝐴 = 30.8𝑔 𝑊𝑤 = 19.5𝑔

𝑆𝐺 =𝑊𝐴


𝑆𝐺 =30.8𝑔

30.8𝑔 − 19.5𝑔

𝑆𝐺 = 2.7257

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =|𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 − 𝐸𝑥𝑝 𝑉𝑎𝑙𝑢𝑒|

𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒× 100%

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =|2.7000 − 2.7257|

2.7000× 100%

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 = 0.9505%

In the second table. The aluminum was the metal

used. This means that the weight in air and water

are already given. The weight of the aluminum

when submerged to the liquids. Observing the

data gathered in Table B, it shows that in the two

unknown liquid samples, the weight of the sample

metal in air is greater than the weight of the

sample metal in water. The reason for this is that

because of the upward buoyant force, water exerts

an upward force, which is the buoyant force,

making the tension due to weight of the sample

metal smaller. Additionally, it can be seen that the

loss of weight in liquid is lesser in sample 2 which

the alcohol than in ample 1 which is water.

Although it is not obvious that it is equal to the

buoyant force of the liquid. The specific gravity of the liquids were computed using the formula: 𝑆𝐺 =𝑊𝐴−𝑊𝐿

𝑊𝐴−𝑊𝑊. The specific gravity was computed and with

these results, it was easy to identify the name of

the unknown liquids which are water and alcohol,

respectively.

TABLE B. Determining the Specific Gravity of

an Unknown Liquid

Sample 1 Sample 2

weight in air, 𝑊𝐴 30.8 g 48.8 g

weight in water, 𝑊𝑤 19.5g 42.8g

weight in liquid, 𝑊𝐿 21.3g 43.5g

Loss of weight in

liquid, 𝑊𝐴 − 𝑊𝐿 9.5g 5.3g

Specific Gravity,

𝑆𝐺 =𝑊𝐴 − 𝑊𝐿


0.8407 0.8833

Name of Sample Water Denatured

Alcohol

Percent Error 15.9292% 11.9561%

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Given: 𝑊𝐴 = 30.8𝑔 𝑊𝑤 = 19.5𝑔 𝑊𝐿 = 21.3𝑔

𝑙𝑜𝑠𝑠 𝑜𝑓 𝑤𝑒𝑖𝑔ℎ𝑡 𝑖𝑛 𝑙𝑖𝑞𝑢𝑖𝑑 = 𝑊𝐴 − 𝑊𝐿

𝑙𝑜𝑠𝑠 𝑜𝑓 𝑤𝑒𝑖𝑔ℎ𝑡 𝑖𝑛 𝑙𝑖𝑞𝑢𝑖𝑑 = 30.8𝑔 − 21.3𝑔 𝑙𝑜𝑠𝑠 𝑜𝑓 𝑤𝑒𝑖𝑔ℎ𝑡 𝑖𝑛 𝑙𝑖𝑞𝑢𝑖𝑑 = 11.5𝑔

𝑆𝐺 =𝑊𝐴 − 𝑊𝐿


𝑆𝐺 =30.8 − 21.3

30.8 − 19.5

𝑆𝐺 = 0.8407



𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =|1 − 0.8407|

1× 100%

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 = 15.9292%

For the third table, the specific gravity of water

and alcohol were obtained by getting the

measurements using the hydrometer. The

percent error we got are 5% for water and

5.8302% for the Denatured Alcohol. It was odd at

first because we know that the specific gravity of

water should be equal to 1. We believed that the

water might have been contaminated already.

TABLE C. Determining the Specific Gravity of

an Unknown Liquid Using Hydrometer

Sample 1 Sample 2

Specific Gravity 0.95 0.835

Name of Sample Water Denatured

Alcohol

Percent Error 5% 5.8302%


𝑆𝐺 = 0.95



𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =|1 − 0.95|

1× 100%

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 = 5%

For materials lighter than water, it is difficult to

determine its specific gravity using Archimedes’

principle since the object will just float in water. In

order to do this, a sinker was used. For the last

table, the cork is the material mainly observed.

The weight of the cork in the electronic balance is

2.3g. When the sinker is submerged in water while

the cork is hanging above the water, the weight is

45.2g. When both the sinker and the cork were

submerged into the water the weight is 33.5g. The

specific gravity was computed using the

formula: 𝑆𝐺 =𝑊𝐴

𝑊𝐶𝐴−𝑆𝑤−𝑊(𝐶+𝑆)𝑤.The specific gravity of

the cork was determined to be 0.1966.

TABLE D. Determining the Specific Gravity of

Solid Lighter than Water

Name of sample: CORK

weight of cork in air, 𝑊𝐴 2.3g

Weight of cork in air and sinker in

water, 𝑊𝐶𝐴−𝑆𝑊 45.2g

Weight of both sinker and cork in in water, 𝑊(𝐶+𝑆)𝑊

33.5g

Specific Gravity,

𝑆𝐺 =𝑊𝐴

𝑊𝐶𝐴−𝑆𝑤 − 𝑊(𝐶+𝑆)𝑤

0.1966

Sample Computation:

Given:

𝑊𝐴 = 2.3𝑔 𝑊𝐶𝐴−𝑆𝑊 = 45.2𝑔 𝑊(𝐶+𝑆)𝑊 = 33.5𝑔

𝑆𝐺 =𝑊𝐴

𝑊𝐶𝐴−𝑆𝑤 − 𝑊(𝐶+𝑆)𝑤

𝑆𝐺 =2.3𝑔

45.2𝑔 − 33.5𝑔

𝑆𝐺 = 0.1966

DISCUSSION & CONCLUSION

In this experiment, we determined the density and

specific gravity of solids and liquids following

Archimedes’ principle. Density and specific gravity

of materials are unique on each object that makes

it as a tool in the identification of the material.

Density is equal to mass over volume. While,

specific gravity on the other hand is the ratio of

the density of the material with the density of the

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reference liquid which is commonly water. When

an object is immersed in liquid, there is a resistant

force present in water pushing up the object. This

is called the buoyant force and it is the reason why

the weight of an object lessens. Furthermore, the

buoyant force is also the weight of the liquid

displaced by the object. Additionally, the loss of

weight in liquid is equivalent to the magnitude of

the buoyant force.

In the first part of the experiment, we have

computed for the specific gravity of unidentified

solid samples such as metals that are heavier than

water. The unknown solid samples are aluminum

and brass. Based on our data, the solid sample

which has greater weight has a greater specific

gravity. The idea of specific gravity of an object

tells us that it is the number of times an object is

denser than water. From our data, brass has

greater weight than aluminum, thus tells us that it

has a greater specific gravity than aluminum too.

The mass of brass is greater than the mass of

aluminum but the aluminum can displace greater

amount of water compared to brass. It is just

because brass is denser than aluminum.

In the second part of experiment, the two

unknown liquid samples were revealed. The

weight of the sample metal in air is greater than

the weight of the sample metal in water. The

science behind it is the buoyant force in

Archimedes’ principle. It can be comprehended in

the table the contrast of the loss of weight among

the two liquids. Alcohol loss less weight than

water. It means alcohol is more buoyant and

denser than water.

In the third part of the experiment, it only verifies

the results we have obtained from the second part

of the experiment. It shows us that when an

apparatus like the hydrometer which is used to

measure the specific gravity of liquids, we can

check if the results we have from the second part

of the experiment is correct. The specific gravity

of alcohol is less than water, which proves that it

is denser than water.

In the last part of the experiment, materials lighter

than water will totally float on water and it is

difficult to submerge and determination of its

specific gravity is a little bit hard that’s why a

sinker was used during this portion of experiment.

Using Archimedes’ principle loss of weight of cork

is simply the buoyant force exerted by the water

to the cork.

In conclusion, when the loss of weight in liquid

increases, expecting that the specific gravity also

increases. It means when the liquid is more

buoyant, the liquid is denser. This density is the

force that rise up the object that is being or totally

immersed that makes the object’s weight smaller.

The possible source of error for the performed

experiment is the inconsistency of the electronic

balance since sometimes it won’t turn on maybe

because of the poor battery and when the

measuring the same material for another try, it

shows a different reading. It is better to make

sure that the electronic balance is in a good

working condition. The next possible source of

error for the experiment that we have experienced

is the impurity of the liquid sample. The liquids

might have been contaminated already.

ACKNOWLEDGMENT & REFERENCE

I would like to thank my groupmates for being so

cooperative upon doing the experiment. I

appreciate all of their efforts since without their

help, our experiment will have a great chance of

failure. I also thank my group mates for making

every experiment filled with humor, since we find

some parts of the experiment difficult to execute,

they are still composed and not pressured because

of time. Thank you for making my physics

laboratory class happy and while learning. I would

also like to thank our professor, Prof. Ricardo F.

De Leon, Jr. for guiding all throughout the

experiment and always giving us plus points. I also

would like to acknowledge the lab assistants for

reminding us how to handle the materials and

equipment and telling us about the important

things to remember when conducting the

experiment and for also being approachable when

we ask for a piece of string. Lastly, I would like to

thank my family for supporting me in my studies

as I pursue my degree in Mapúa.

References:

General Physics 2 Laboratory Manual, Mapúa

Institute of Technology, Manila: Department of

Physics.

Walker, J., Halliday, D., & Resnick, R. (2014).

Principles of Physics. 10th Edition. 395-397.

Buoyancy. Retrieved (September2015).

https://en.wikipedia.org/wiki/Buoyancy

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Osbourne, J. Archimedes’ Principle, Retrieved

(September 2015).

http://www.brightstorm.com/science/physics/osc

illatory-motion/archimedes-principle

Srinivas, A. Archimedes Principle and Battery

Indicators, Retrieved (September 2015).

http://www.physics247.com/physics-

tutorial/archimedes-principle.shtml

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