Determining the Relative Density of an Object in Water

Introduction

Understanding the relative density (or specific gravity) of an object is fundamental in many fields such as chemistry, physics, and engineering. This article explores how to determine the relative density of an object using its weight in air and in water. The principles of buoyant force and Archimedes' Principle will guide us in the process.

Background Information

Relative density (RD) is defined as the ratio of the density of a substance to the density of a reference substance, typically water. The density of water is usually taken as 1000 kg/m3. Archimedes' Principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. This principle is crucial in understanding how objects behave in various fluids.

Experimental Data

We have an object with the following weight data in air and water:

Weight in air: 100 N Weight in water: 20 N

Calculations

To determine the density of the object, we start by calculating the buoyant force (BF). According to Archimedes' Principle, the buoyant force is equal to the difference in weight of the object when it is in air and when it is in water:

Buoyant Force (BF) Weight in air - Weight in water 100 N - 20 N 80 N

Using the formula for buoyant force, BF Vdg, where V is the volume of the displaced fluid, d is the density of water, and g is the gravitational acceleration (9.8 m/s2), we can solve for the volume of the displaced water:

80 N V times; 1000 kg/m3 times; 9.8 m/s2

V 80 N / (1000 kg/m3 times; 9.8 m/s2) ≈ 0.008163 m3

This volume is also the volume of the submerged object.

Next, we calculate the mass of the object using the weight in air and gravitational acceleration:

Weight in air mg

100 N m times; 9.8 m/s2

m 100 N / 9.8 m/s2 10.2 kg

Using the mass and the volume, we can now calculate the density of the object:

Density of object mass / volume

Density of object 10.2 kg / 0.008163 m3 ≈ 1250 kg/m3

The density of the object is approximately 1250 kg/m3.

Conclusion

In summary, the relative density of an object can be determined using the principles of Archimedes' Principle and buoyant force. By knowing the weight of an object in air and in water, we can calculate the mass and the volume of the displaced water, which leads to the density of the object. This method is particularly useful in various scientific and engineering applications.

References