The Mystery of Gold's Weight in Air vs. Water: Exploring Archimedes' Principle

When considering the weight of one kilogram (kg) of gold in air versus water, a fascinating concept emerges: while the mass of gold remains constant, its apparent weight changes due to the principle of buoyancy. This article delves into the science behind this phenomenon and highlights the importance of understanding Archimedes' principle in everyday situations.

Weight of Gold in Air

The weight of one kilogram of gold in the air is a straightforward calculation based on its mass and the acceleration due to gravity, denoted as g. The formula to determine the weight in air is given by:

Weight in air mass × g 1 kg × 9.81 m/s2 9.81 N

This result shows that the weight of one kilogram of gold in air is 9.81 Newtons (N).

The Impact of Buoyancy

However, when this same gold is submerged in water, something interesting happens due to the principle of buoyancy, as described by Archimedes. When an object is immersed in a fluid, it experiences an upward force called the buoyant force, which is equal to the weight of the fluid displaced by the object.

Buoyant Force Calculation for Gold in Water

To understand the buoyant force acting on the gold, let's first determine the volume of one kilogram of gold. The density of gold is approximately 19,320 kg/m3, while the density of water is about 1,000 kg/m3.

Calculate the volume of 1 kg of gold:

Volume mass / density 1 kg / 19,320 kg/m3 ≈ 0.0000518 m3

Calculate the weight of the water displaced by the gold:

Weight of the water displaced volume × density of water 0.0000518 m3 × 1,000 kg/m3 0.0518 kg

Convert this weight to Newtons:

Weight of the water displaced in N 0.0518 kg × 9.81 m/s2 ≈ 0.508 N

Now, subtract the buoyant force from the weight in air to determine the apparent weight of the gold in water:

Apparent weight weight in air - buoyant force 9.81 N - 0.508 N ≈ 9.302 N

Gold's Apparent Weight Compared to Its Value

Interestingly, the apparent weight of the gold in water is approximately 9.302 N, even though its mass remains 1 kg. This apparent reduction in weight is due to the buoyant force acting upwards, which is equal to the weight of the water displaced by the gold.

Understanding Gold's Density and Buoyancy

Gold's density being 19.3 times that of water offers additional insights. If you calculate the volume of gold that weighs 1 kg using its density (19,320 kg/m3):

Volume of gold 1 kg / 19,320 kg/m3 ≈ 0.0000518 m3 51.8 cc (cubic centimeters)

The weight of the water displaced by this volume of gold is:

Weight of water displaced 51.8 cc × 1 g/cc 51.8 g

Thus, the weight of gold in water is 1,000 g (1 kg) - 51.8 g 948.24 g.

When hanging 1 kg of gold on a spring scale in water, the scale would show a weight of approximately 0.948 kg.

Archimedes' Principle in Operation

Archimedes' principle, which states that the upward buoyant force on an object is equal to the weight of the fluid displaced by the object, plays a crucial role in this phenomenon. For 1 kg of gold:

Volume of gold 52 cm3 Weight of gold 1,000 g Weight of water displaced 52 g Weight of gold in water 1,000 g - 52 g 948 g

Conclusion

The weight of one kilogram of gold in air and water differs due to the principle of buoyancy as explained by Archimedes. While the mass remains constant, the apparent weight changes. This phenomenon is not only intriguing but also has practical applications in various fields, including jewelry, mining, and scientific research. Understanding these principles helps in accurately measuring and evaluating the properties of materials.