PHY11L A4 E206

E206: ARCHIMEDES’ PRINCIPLE FRISNEDI, Nadine T.

OBJECTIVE

MATERIALS AND METHODS

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.

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).

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. Figure 1. Materials and equipment used in the experiment.

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.

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 1|Page

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.

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

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.

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 . The same procedures were repeated using 𝑊𝐴 −𝑊𝑊

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

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 2|Page

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 𝑊 −𝑊 equation: 𝑆𝐺 = 𝐴 𝐿 . Using a different liquid 𝑊𝐴 −𝑊𝑊

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. 3|Page

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: 𝑊𝐴 𝑆𝐺 = .

𝑆𝐺 = 2.7257 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =

OBSERVATIONS AND RESULTS

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, 𝑊𝐴 𝑆𝐺 = 𝑊𝐴 − 𝑊𝑊

2.7257

8.1333

Name of Sample

Aluminum

Brass

Percent Error

0.9505%

3.6335%

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 . The specific gravity was computed and with 𝑊𝐴 −𝑊𝑊

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

9.5g

5.3g

0.8407

0.8833

Water

Denatured Alcohol

15.9292%

11.9561%

Loss of weight liquid, 𝑊𝐴 − 𝑊𝐿 Specific Gravity, 𝑊𝐴 − 𝑊𝐿 𝑆𝐺 = 𝑊𝐴 − 𝑊𝑊 Name of Sample

𝑆𝐺 =

𝑊𝐴 𝑊𝐴 − 𝑊𝑊

|2.7000 − 2.7257| × 100% 2.7000

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 = 0.9505%

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 𝑊𝐴 computed using the equation: 𝑆𝐺 = .

Given: 𝑊𝐴 = 30.8𝑔 𝑊𝑤 = 19.5𝑔

|𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 − 𝐸𝑥𝑝 𝑉𝑎𝑙𝑢𝑒| × 100% 𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =

𝑊𝐶𝐴−𝑆𝑤 −𝑊(𝐶+𝑆)𝑤

Sample Computation for Sample 1

30.8𝑔 30.8𝑔 − 19.5𝑔

𝑆𝐺 =

Percent Error

in

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Sample Computation for Sample 1 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 𝑊𝐴 − 𝑊𝐿 𝑊𝐴 − 𝑊𝑊 30.8 − 21.3 𝑆𝐺 = 30.8 − 19.5 𝑆𝐺 =

𝑊𝐶𝐴−𝑆𝑤 −𝑊(𝐶+𝑆)𝑤

the cork was determined to be 0.1966. TABLE D. Determining the Specific Gravity of Solid Lighter than Water

𝑆𝐺 = 0.8407 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =

|𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 − 𝐸𝑥𝑝 𝑉𝑎𝑙𝑢𝑒| × 100% 𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒

|1 − 0.8407| 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 = × 100% 1 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%

Sample Computation for Sample 1 𝑆𝐺 = 0.95 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =

|𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 − 𝐸𝑥𝑝 𝑉𝑎𝑙𝑢𝑒| × 100% 𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =

|1 − 0.95| × 100% 1

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 𝑊𝐴 formula: 𝑆𝐺 = .The specific gravity of

Name of sample: CORK weight of cork in air, 𝑊𝐴 Weight of cork in air and sinker in water, 𝑊𝐶𝐴−𝑆𝑊 Weight of both sinker and cork in in water, 𝑊(𝐶+𝑆)𝑊 Specific Gravity, 𝑊𝐴 𝑆𝐺 = 𝑊𝐶𝐴−𝑆𝑤 − 𝑊(𝐶+𝑆)𝑤

2.3g 45.2g 33.5g 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 5|Page

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 6|Page

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/physicstutorial/archimedes-principle.shtml

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