Weight - Gravity's Pull on Mass
In everyday language people use the word "weight" to mean how heavy something is. In science, weight and mass are completely different things. Understanding this distinction matters in physics, engineering, and space exploration.
The formula W = mg comes directly from the work of Sir Isaac Newton, who published his law of universal gravitation in 1687 in a book called the Principia Mathematica – showing that the same force pulling an apple to the ground also keeps the Moon in orbit around the Earth. The unit of weight, the Newton (N), was named in his honour more than 200 years later. The mass-versus-weight distinction became front-page science during the Apollo Moon landings: astronauts carrying the same bulky equipment felt roughly six times lighter on the Moon's surface (since the Moon's gravity is about one-sixth of Earth's), even though their mass, and the equipment's mass, had not changed by a single gram – famously letting them bound across the lunar surface in long, low leaps.
Mass vs Weight
| Mass | Weight | |
|---|---|---|
| Definition | Amount of matter in an object | Force due to gravity acting on mass |
| Unit | Kilogram (kg) or gram (g) | Newton (N) |
| Changes with gravity? | No – constant everywhere | Yes – varies by location |
| Instrument | Balance scale | Spring balance / newton meter |
The Weight Formula
Weight = Mass × Gravitational field strength
W = m × g (W in Newtons, m in kg, g in N/kg)
On Earth: g ≈ 9.81 N/kg (often rounded to 10 N/kg for quick estimates).
How Weight Varies by Location
| Location | g (N/kg) | Weight of a 60 kg person |
|---|---|---|
| Earth | 9.81 | 588.6 N |
| Moon | 1.62 | 97.2 N |
| Mars | 3.72 | 223.2 N |
| Jupiter | 24.79 | 1,487.4 N |
| Deep space | 0 | 0 N (weightless) |
Worked Examples
W = 70 × 9.81 = 686.7 N.
W = 70 × 1.62 = 113.4 N. Their mass is still 70 kg – only the weight changes.
m = W ÷ g = 49 ÷ 9.81 ≈ 5 kg.
W = 25 × 10 = 250 N.
Key Takeaways
- Mass is measured in kg and stays constant everywhere.
- Weight is a force measured in Newtons: W = m × g.
- On Earth g ≈ 9.81 N/kg. On the Moon g ≈ 1.62 N/kg.
- An astronaut in orbit is weightless but still has the same mass as on Earth.