The difference between weight in a vacuum and weight outside a vacuum (e.g., in air or another medium) primarily stems from the effect of buoyancy and the presence of a surrounding medium.
1. Weight in a Vacuum
- Definition: Weight is the force exerted by gravity on a mass. In a vacuum, there is no air or other medium to affect the measurement.
- Measurement: In a vacuum, an object’s weight is simply the product of its mass and the gravitational acceleration (W = m × g). This is the true weight of the object.
- Example: A 1 kg object in a vacuum on Earth, where g ≈ 9.8 m/s², has a weight of 9.8 Newtons.
2. Weight Outside a Vacuum (e.g., in Air)
- Buoyancy Effect: When an object is weighed in air (or any fluid medium), it is partially supported by the buoyant force due to the displacement of the surrounding medium. According to Archimedes’ principle, the buoyant force equals the weight of the fluid displaced by the object.
- Apparent Weight: The weight measured in air is the apparent weight, which is slightly less than the true weight because the buoyant force reduces the force registered by a scale.
- Formula: Apparent weight = True weight – Buoyant force
- Buoyant force = (Density of air) × (Volume of the object) × (Gravitational acceleration).
- Example: For a 1 kg object with a volume of 0.001 m³ in air (density of air ≈ 1.2 kg/m³), the buoyant force is approximately:
- Buoyant force = 1.2 kg/m³ × 0.001 m³ × 9.8 m/s² = 0.01176 N.
- True weight = 9.8 N, so apparent weight = 9.8 N – 0.01176 N ≈ 9.788 N.
Key Differences
| Aspect | Weight in Vacuum | Weight Outside Vacuum (e.g., in Air) |
|---|---|---|
| Environment | No surrounding medium (no air/fluid). | Surrounded by air or another medium. |
| Buoyancy | No buoyant force (no medium to displace). | Buoyant force reduces apparent weight. |
| Measurement | True weight (W = m × g). | Apparent weight (slightly less than true weight). |
| Accuracy | Reflects the exact gravitational force. | Slightly less due to buoyancy. |
| Example (1 kg object) | 9.8 N (true weight). | ~9.788 N (apparent weight, depending on volume). |
Practical Implications
- Small Effect in Air: For most objects, the buoyant force in air is negligible because air density is low (e.g., ~1.2 kg/m³). The difference between true and apparent weight is typically less than 0.1% unless the object has a very low density or large volume.
- Significant in Liquids: If the object is weighed in a denser medium like water (density ≈ 1000 kg/m³), the buoyant force is much larger, and the apparent weight is significantly reduced.
- Applications: In precise measurements (e.g., scientific experiments or high-precision scales), weights are often calibrated in a vacuum or corrected for buoyancy to ensure accuracy.
Summary
- In a vacuum, you measure the true weight (mass × gravity).
- Outside a vacuum (e.g., in air), you measure the apparent weight, which is slightly less due to the buoyant force of the surrounding medium.
- The difference is usually small in air but can be significant in denser fluids or for objects with large volumes or low densities.
