Archimedes’ Principle Experiment: Determining Gravity of Objects

Experimental Objectives

• To determine the specific gravity of different metallic objects that are denser than water
• To determine specific gravity of a liquid
• To determine the specific gravity of wood which is less dense which water is denser that it

Theory

By definition, density ρ₀ of a substance is “a physical property of matter that is defined as the ratio of an object’s mass to its volume” (Day and Carpi 1). Density does not dependent on the quantity of an object. It is given by the equation: _ρ0 = m/V (1)

On the other hand, specific gravity is dependent on the amount or quantity of a substance and is defined as “the ratio of the density of an object to the density of water ρw at 4°C” (Day and Carpi 2). Since specific gravity is a ratio of two densities, it is a dimensionless attribute. Specific gravity is given by the expression:

Specific Gravity = SG = ρ0 / ρw = m / m-m1 (2)

Where m=mass of the object, m₁=the apparent mass of object in a fluid.

According to Weinstein, Archimedes’ principle asserts that a substance placed in a fluid (liquid or gas) experiences an upward buoyant force from the fluid. This force is equal to the weight of the fluid displaced by the object (2). When a substance is placed on a liquid there are 3 possibilities: 1) it can float on water if its less dense than the liquid it is placed on. 2) It will be submerged in the liquid to a deepness that is adequate to dislocate the heaviness of the fluid equivalent to its individual heaviness, 3) it will sink to the bottom of a fluid if denser. Therefore, in simple words, the principle says that the weight of water is equivalent to the floating force that is: B = m_wg = ρ_wV_wg = ρ_wV₀g (2)

Results

For objects with density greater than that of water, the following results were obtained:

From equation 2, which describes specific gravity of objects, we calculate the specific densities as follows:

Copper, SG= (56.60)/ (56.60-49.52) =7.99

Percentage error in copper = (0.91X100)/8.90=10%

Zinc=, SG= (29.10)/ (56.60-28) =7.89

Percentage error in zinc = (0.79X100)/7.10=12%

For objects, whose density is less than that water. The sample objects were measured and recorded as follows:

Table 2

Using equation: SG = W / W1-W2 = mg / m1g – m2g = m / m1 – m2

Where m=mass of object, m₁= the apparent mass with the object in air and a sinker submerged in water and m₂= the apparent mass with the object and the sinker submerged in water. We compute density of wood as follows:

SG _wood= 7.50/ (436-434) =3.75

For liquid with unknown specific gravity, the experiment was performed and recorded as follows:

Table 3

Using equation, SG (liquid) = m – ml / m – mw

where in this case, m=mass of copper, ml=apparent mass of copper in alcohol and mw =apparent mass in water. We compute the results in the table below:

Questions

1. Describe your results- by measuring force exert on different objects immersed in water or any fluid, Archimedes’ Principle was used to determine the specific gravity of zinc and copper in water, wood in water and wood in alcohol. specific gravity of Zinc was found to b 7.89 with an error percentage of 12 while that of copper as 7.99 with an error percentage of 10(where they are denser than water). On the other hand, when the substance is less dense for example, wood, the experiment was modified, and specific gravity found out to be 3.75
2. An object whose specific gravity is 0.900 is placed in a liquid whose specific gravity is 0.900. Describe how the object will behave. In other words, will it sink or float, or what will be its behavior? Answer: since the they have equal specific gravity; the object will sink in the liquid to a deepness that is enough to displace the heaviness of the fluid equivalent to its own weight.
3. An object whose specific gravity is 0.850 is placed in water. What fraction of the object is below the surface of the water? Since specific gravity a ratio between densities of a substance and in this case the substance has specific gravity less than one, the object will float and therefore zero fraction will be below water.
4. Alternative derivation of the equation: SG = p0 / pw = m / m-m1 (7) and SG = W / W1-W2 = mg / m1g – m2g = m / m1 – m2 (13)
5. An object has a mass in air of 0.0832 kg, apparent mass in water of 0.0673 kg, and apparent mass in another liquid of 0.0718 kg. What is the specific gravity of the other liquid? From the equation SG (liquid) = m – ml / m – mw. We put in respective figures to find the specific gravity of the object as follows: SG (liquid) = 0,0832 – 0,0,718 / 0,0832 – 0,0673 = 0,71698 = 0,7170

Conclusion

Using Archimedes’ Principle, we have been able to determine specific gravity of Zinc as 7.89 with an error percentage of 12 while that of copper as 7.99 with an error percentage of 10(where they are denser than water). On the other hand, when the substance is less dense for example, wood, the experiment was modified, and specific gravity found out to be 3.75. Archimedes’ Principle is a value principle that helped us determine specific gravity of different substances in different fluid i.e., water and alcohol. Since the specific gravities of wood, copper, and zinc were determined, the objects of the experiment were achieved.

References

Day, Martha and Carpi, Anthony.” Density.” Vision learning Journal, 23.2(2002):1-7.

Weisstein, Eric. Archimedes’ Principle. New York, NY: Prentice Hall, 2007. Print.