Calculating the Specific Gravity of Cork

The specific gravity (S.G.) of cork is a critical parameter in determining its buoyancy and application in various industries. This article delves into the process of calculating the specific gravity of cork using both traditional and modern methods, ensuring a comprehensive understanding of the concept.

Understanding Specific Gravity in Cork

Specific gravity (S.G.) is the ratio of the density of a substance to the density of a reference substance. For most practical purposes, water at 4°C (1 g/cm3) is the reference substance. It is often used to compare the relative density of different substances. In the case of cork, its specific gravity provides valuable insights into its buoyancy and applicability in various contexts.

Traditional Calculation Method

For a piece of cork with a mass of 4 kg, floating with 40% of its volume submerged in water, the specific gravity can be calculated using a series of steps based on Archimedes' principle and basic physics principles.

Steps to Calculate Specific Gravity

Determine the volume of the submerged portion of the cork.

Given that 40% of the cork's volume is submerged, let the total volume of the cork be (V). Therefore, the volume of the submerged portion is (0.4 times V).

Calculate the buoyant force acting on the cork.

According to Archimedes' principle, the buoyant force is equal to the weight of the displaced water. The weight of the displaced water is given by the density of water (1 g/cm3) multiplied by the volume of the submerged portion. Thus, the buoyant force is:

(F_b 1 text{ g/cm}^3 times 0.4 times V)

Calculate the weight of the cork.

The weight of the cork is given by its mass (4 kg) multiplied by the acceleration due to gravity (9.8 m/s2). Thus, the weight of the cork is:

(F_g 4 text{ kg} times 9.8 text{ m/s}^2 39.2 text{ N})

At equilibrium, the buoyant force equals the weight of the cork.

Hence, (F_b F_g), which means:

(1 text{ g/cm}^3 times 0.4 times V 39.2 text{ N})

Solve for the total volume of the cork (V).

(V frac{39.2 text{ N}}{1 text{ g/cm}^3 times 0.4} 98 text{ cm}^3)

Calculate the density of the cork.

The density of the cork is given by the mass of the cork divided by its volume:

(rho frac{4 text{ kg}}{0.098 text{ m}^3} 40.82 text{ kg/m}^3)

Calculate the specific gravity of the cork.

The specific gravity is the density of the cork divided by the density of water (1000 kg/m3):

(text{S.G.} frac{40.82 text{ kg/m}^3}{1000 text{ kg/m}^3} 0.4082)

Thus, the specific gravity of cork is 0.4082.

Modern Calculation Method

The modern approach to calculating specific gravity involves a simpler mathematical relationship based on the principle of buoyancy as described by Archimedes.

The mass of the cork can be expressed in two ways:

(m rho_c V), where (rho_c) is the density of the cork and (V) is its volume. (m 0.4 V d), where (d) is the density of water (1 g/cm3).

By equating the two expressions and solving for (rho_c), we get:

(rho_c 0.4 text{ g/cm}^3)

This shows that the density of cork is 0.4 g/cm3, and hence, its specific gravity is 0.4.

Conclusion

Calculating the specific gravity of cork is an essential task in understanding its physical properties and applications. Whether using the traditional method involving the density and volume of the cork or the modern method based on Archimedes' principle, the result remains the same. The specific gravity of cork is a fundamental parameter that helps in various industries, including the production of sustainable materials and buoyancy applications.