Diving Deeper into Density: Calculating Weight Underwater

Understanding the principles of density and buoyancy can be crucial in various fields, from understanding the behavior of objects in fluids to its applications in engineering and science. In this article, we will explore the fascinating world of density and buoyancy by solving a problem involving the weight of an object when it is fully submerged in water.

Introduction to Density and Buoyancy

Density is a fundamental physical property that measures the mass per unit volume of a substance. It is defined as the ratio of an object's mass to its volume. In liquid mechanics, buoyancy arises when a fluid exerts an upward force on an object that is either wholly or partially submerged in it. This force is essentially the weight of the fluid that the object displaces.

The Problem at Hand

Consider an object that has a weight of 21 kg in air. Its relative density (also known as specific gravity) is given as 4.8. The density of water is 1000 kg/m3. The task is to find the weight of the object when it is fully immersed in water. To solve this, we need to delve into the principles of density and buoyancy.

Understanding Relative Density

Relative density (specific gravity) is the ratio of the density of a substance to the density of a reference substance, which we will take as water in this case. Hence, the formula for relative density is:

Relative Density frac{Density of Object}{Density of Water}

Using the given values:

4.8 frac{text{Density of Object}}{1000}

This simplifies to:

text{Density of Object} 4800 text{ kg/m}^3

Calculating the Up Thrust

Now that we have the density of the object, we can calculate the up thrust it experiences in water. The up thrust, also known as the buoyant force, is equal to the weight of the water displaced by the object. The formula for the up thrust is:

Up Thrust text{Volume of Object} times text{Density of Water} times g

However, we can also express the up thrust in terms of the object's weight in air and its relative density:

Up Thrust text{Volume of Object} times text{Density of Object} times g frac{text{Weight of Object}}{text{Relative Density}} frac{Weight in Air}{text{Relative Density}}

In this problem, the up thrust is:

Up Thrust frac{21 text{ kg}}{4.8} approx 4.38 text{ kg}

Finding the Weight Underwater

When the object is immersed in water, the net weight (weight in water) can be found by subtracting the up thrust from the weight in air:

Weight in Water Weight in Air - Up Thrust 21 text{ kg} - 4.38 text{ kg} approx 16.62 text{ kg}

This calculation shows that the weight of the object when fully immersed in water would be approximately 16.62 kg.

Conclusion

Through this problem, we have gained a deeper understanding of the principles of density and buoyancy. By calculating the weight of the object when it is fully submerged in water, we reinforce our understanding of these important concepts. The exercise not only sharpens our mathematical skills but also provides a practical application of scientific principles.

Practice Makes Perfect

Now, it is your turn to practice! Use the steps we discussed to solve similar problems and solidify your understanding of density and buoyancy. Remember, the key to mastering these concepts is to practice and apply them in various scenarios.