Objects have different weights in water and air due to buoyancy, a force exerted by fluids that affects an object's apparent weight.
1. Weight in Air
- In air, an object’s weight is its true weight, determined by its mass and the gravitational force acting on it (Weight = Mass × Gravity, or W = m × g).
- Air is a low-density medium, so the buoyant force it exerts is negligible for most objects. Thus, the measured weight in air is essentially the object’s actual weight.
2. Weight in Water
- When an object is submerged in water, it experiences an upward buoyant force due to the water displaced by the object. This is known as Archimedes’ Principle, which states: The buoyant force on an object is equal to the weight of the fluid displaced by the object.
- The buoyant force reduces the object’s apparent weight (the weight measured in water). The apparent weight is calculated as: Apparent Weight = True Weight – Buoyant Force
- The buoyant force depends on:
- Volume of the object: The more water displaced, the greater the buoyant force.
- Density of the fluid: Water is much denser than air, so the buoyant force in water is significant compared to air.
- Gravitational acceleration: This remains constant in both mediums.
3. Why the Difference?
- In water, the object displaces a volume of water, which has significant weight due to water’s high density (about 1000 kg/m³). This creates a noticeable buoyant force that counteracts the object’s weight, making it feel lighter.
- In air, the density (about 1.2 kg/m³) is much lower, so the buoyant force is minimal and usually ignored for practical purposes.
- For example, a 1 kg object with a volume of 0.001 m³ (1 liter) displaces 1 kg of water when fully submerged, resulting in a buoyant force of 9.8 N (weight of 1 kg of water). In air, the same object displaces only about 0.0012 kg of air, producing a negligible buoyant force of ~0.012 N.
4. Key Factors Affecting Weight Difference
- Object Density: If the object is less dense than water (e.g., wood), it may float, and the buoyant force can equal or exceed its weight. If denser (e.g., steel), it sinks but still experiences buoyancy.
- Submersion Level: If the object is only partially submerged, the buoyant force is proportional to the volume of water displaced.
- Fluid Medium: Different fluids (e.g., saltwater vs. freshwater) have different densities, affecting the buoyant force.
5. Practical Examples
- Swimming: Humans feel lighter in water because buoyancy supports part of their weight.
- Submerged Objects: A heavy rock is easier to lift underwater due to the buoyant force reducing its apparent weight.
- Hydrometers: These devices measure fluid density by floating at different levels, leveraging buoyancy.
6. Mathematical Representation
- True weight in air: W = m × g
- Buoyant force in water: F_b = ρ_water × V × g (where ρ_water is water density, V is the volume of the object submerged)
- Apparent weight in water: W_apparent = W – F_b = m × g – ρ_water × V × g
