Determining the Density of a Metal Spoon Using Buoyancy

Welcome to our guide on determining the density of a metal spoon using the principles of buoyancy. This article explains how to calculate the density of a metal spoon given its weight in air and in water. By following these steps, you can better understand the relationship between weight, volume, and density.

Understanding Buoyancy and Density

Buoyancy is the upward force exerted by a fluid on an object immersed in it. This force is equal to the weight of the fluid displaced by the object. Understanding the relationship between buoyancy and density is crucial for calculating the density of objects immersed in different fluids.

Calculating the Volume of the Metal Spoon

Given the weight of the metal spoon in air (0.48 N) and in water (0.42 N), we can calculate its weight loss in water. This loss is due to the buoyant force, which is equal to the weight of the water displaced by the spoon.

Step 1: Calculate the weight loss in water
Weight loss in water Weight in air - Weight in water
0.48 N - 0.42 N 0.06 N

Step 2: Convert the weight loss to volume
The weight of the displaced water can be used to find the volume since we know the density of water (1000 kg/m3) and the acceleration due to gravity (9.81 m/s2).

Weight loss Volume × Density of water × g
0.06 N Volume × 1000 kg/m3 × 9.81 m/s2

Rearranging to find volume:
Volume 0.06 N / (1000 kg/m3 × 9.81 m/s2) ≈ 6.11 × 10-6 m3

Calculating the Mass of the Metal Spoon

To find the mass of the spoon, we use its weight in air. The weight of an object is related to its mass by the formula:

Weight in air Mass × g
0.48 N Mass × 9.81 m/s2

Solving for mass:
Mass 0.48 N / 9.81 m/s2 ≈ 0.0489 kg

Calculating the Density of the Metal Spoon

With both the mass and volume known, the density can be calculated using the formula:

Density Mass / Volume
7993 kg/m3 0.0489 kg / 6.11 × 10-6 m3

Alternative Calculation:
Another method involves using the buoyant force. Here, we can also find the volume from the buoyant force, which is the difference in weight in air and in water (0.06 N). This is equal to the weight of the displaced water.
0.06 N V × 1000 kg/m3 × 9.81 m/s2 / 1000
Volume 0.06 / (1000 kg/m3) ≈ 6.33 g/cm3

Therefore, the density of the metal spoon is approximately 7993 kg/m3.

Frequently Asked Questions

What is buoyancy? Buoyancy is an upward force exerted by a fluid on an object immersed in it, equal to the weight of the fluid displaced by the object. How does buoyancy relate to density? Objects less dense than the fluid float due to buoyancy, while objects denser than the fluid sink, displacing an amount of fluid whose weight is equal to the object’s. Why is the weight in water different from the weight in air? The weight in water is less because of the buoyant force. The spoon displaces an amount of water, which pushes up on the spoon, effectively reducing its weight.

References

- The Archimedes Principle TheNikonGuy - Understanding Buoyancy and the Archimedes Principle Khan Academy - Buoyancy and Density