Study the Relation between Loss in weight of Solid in Tap water and in Salty water

# Objective

To establish the relation between the loss in weight of solids when fully immersed (i) in tap water and (ii) in strongly salty water and the weight of water displaced by it by taking at least two different solids.

# Theory

Have you ever felt lighter while swimming? Observe the pictures given below.

Figure 1(a) An object is submerged in a fluid.                                        Figure 1(b) An object is removed from the fluid.

Imagine a scenario where you find yourself immersed or submerged in water, as illustrated in Figure 1(a).

In this context, when your body (object) is submerged in water (fluid), the weight of the object (Wobj) is directed downward due to gravitational force. Simultaneously, the fluid exerts an upward buoyant force (Fb) on the object. This buoyant force, also known as upthrust, is a result of the fluid's upward pressure on the immersed object.

The weight of an object is essentially the force due to gravitational pull. When immersed in a fluid, the object displaces the fluid. The interaction between the buoyant force and the gravitational force (weight) of an object might result in two different outcomes:

• If the buoyant force exerted on an object submerged in a fluid is greater than the gravitational force acting upon the object (its weight), the object rises.
• If the buoyant force exerted on an object submerged in a fluid is less than the gravitational force acting upon the object (its weight), the object sinks.

The interaction between gravitational and buoyant forces determines the behavior of the object when it is submerged in the fluid.

Now considering the scenario depicted in Figure 1(b), upon the removal of the object from the fluid, it is replaced by a volume of fluid that has the weight denoted as Wfl. In this specific context, the buoyant force equals the weight of the displaced fluid.

It is explained by Archimedes’ Principle.

## Archimedes’ Principle

When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.

Buoyant force (Fb)= ρVg

ρ = density of fluid

V =  volume of fluid displaced

g = acceleration due to gravity

It is evident that the buoyant force is directly proportional to the density of the fluid. For example, in situations (Fig 2(a) and Fig 2 (b)) where the density of saltwater exceeds that of pure water, the buoyant force in saltwater proportionally increases.

Figure 2(a) Measuring the weight of the object when it is immersed in water

(b) Measuring the weight of the object when it is immersed in salt water

### Loss of weight

When an object is submerged in a fluid, it experiences a reduction in weight compared to its weight in the air. This is attributed to the buoyant force applied by the fluid. This phenomenon is commonly referred to as the loss of weight, and the measured weight of the object in the fluid is termed its apparent weight.

Apparent weight of an object = Actual weight of an object – Buoyant force

When an object is immersed in a fluid, it displaces an amount of fluid equal to its volume.

Furthermore, the loss in the weight of the object is related to the buoyant force, which is equivalent to the weight of the displaced water. The complex connection between changes in fluid density and buoyant forces highlights how they directly impact the apparent weight of the object.

For example, in situations (Fig 2(a) and Fig 2 (b)) where the density of saltwater exceeds that of pure water, the loss in weight of the object is larger in salt water. The apparent weight of the object is larger in tap water.

Why do some materials sink, and others float on water?

Observe Figure 3, which shows how a cork floats on the surface of water, whereas an iron nail quickly sinks under the same circumstances. What is the reason behind this?

Figure 3: An iron nail sinks and cork floats when placed on the surface of the water

Reasons:

• The behavior of the iron nail in Figure 3 is influenced by its weight, which exceeds the buoyant force acting upon it. This is due to the higher density of the iron nail compared to that of water, causing it to sink when placed in the liquid.
• In contrast, in the same situation, the cork experiences a buoyant force that exceeds its weight. The cork's ability to float on the water's surface is attributed to its lower density compared to water.

This phenomenon highlights a general principle: denser objects tend to sink in liquids, while objects with a lower density than the liquid will float.

# Learning Outcomes

The student

• Comprehends the concept of buoyancy.
• Learns about the principle of Archimedes.
• Understands the correlation between density and buoyant force.