Understanding Weight in Water vs. Air

When we weigh an object, we are essentially measuring the force of gravity pulling it downwards. This is often called its true weight or weight in air. However, when an object is submerged in a fluid like water, another force comes into play, opposing the downward pull of gravity. This force is known as the buoyant force.

What is Buoyant Force?

Buoyant force is the upward force exerted by a fluid on an object submerged in it. This force exists because the pressure in a fluid increases with depth. The pressure exerted on the bottom surface of a submerged object is greater than the pressure exerted on its top surface. This pressure difference results in a net upward force – the buoyant force.

How Buoyant Force Affects Apparent Weight

When an object is in air, the buoyant force from the air is usually very small and often negligible. Its weight measured in air is approximately its true weight. When the object is submerged in water, the buoyant force exerted by the water is significant because water is much denser than air.

The buoyant force acts upwards, opposing the object's weight (which acts downwards). The reading on the weighing scale when the object is submerged in water is its apparent weight. The apparent weight is the difference between the true weight and the buoyant force.

This relationship can be expressed with the following formula:

\(W_{apparent} = W_{true} - F_{buoyant}\)

Where:

• \(W_{apparent}\) is the apparent weight of the object when submerged in water.
• \(W_{true}\) is the true weight of the object (its weight in air).
• \(F_{buoyant}\) is the buoyant force exerted by the water on the object.

Since the buoyant force (\(F_{buoyant}\)) acting on a submerged object in water is always greater than zero, the apparent weight (\(W_{apparent}\)) will always be less than the true weight (\(W_{true}\)).

Conclusion: Weight Decreases in Water

Therefore, when an object is weighed while submerged in water, its weight, as measured by the scale (its apparent weight), will be less than its weight in air (its true weight). The buoyant force effectively reduces the downward pull that the scale measures.

Because \(F_{buoyant}\) is positive for a submerged object, \(W_{apparent}\) is less than \(W_{true}\). Thus, the weight decreases when submerged in water.

Revision Table: Key Concepts

Additional Information: Archimedes' Principle and Density

The magnitude of the buoyant force is precisely given by Archimedes' Principle. This principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object.

\(F_{buoyant} = \text{Weight of displaced fluid}\)

The weight of the displaced fluid depends on its volume and density. If the object is fully submerged, the volume of displaced fluid is equal to the volume of the object. If the object is only partially submerged (like a floating object), the volume of displaced fluid is equal to the volume of the submerged part of the object.

The density of the fluid is crucial. Denser fluids exert a greater buoyant force for the same volume displaced. This is why the buoyant force in water is much larger than in air, causing a noticeable decrease in apparent weight.

An object will sink if its weight is greater than the maximum buoyant force the fluid can exert (when the object is fully submerged). It will float if its weight is less than or equal to the buoyant force when only partially submerged.