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.
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
Find the weight of a 70 kg person on Earth. Use g = 9.81 N/kg.
W = 70 × 9.81 = 686.7 N.
The same person travels to the Moon where g = 1.62 N/kg. Find their weight.
W = 70 × 1.62 = 113.4 N. Their mass is still 70 kg – only the weight changes.
An object weighs 49 N on Earth. Find its mass. Use g = 9.81 N/kg.
m = W ÷ g = 49 ÷ 9.81 ≈ 5 kg.
Use g = 10 N/kg to find the weight of a 25 kg bag of cement.
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.
Practice Questions
- Calculate the weight of a 50 kg object on Earth. Use g = 9.81 N/kg.
- On Mars (g = 3.72 N/kg), what is the weight of a 90 kg astronaut?
- An object has a weight of 147 N on Earth. Find its mass. Use g = 9.81 N/kg.
- A 10 kg dumbbell is taken to the Moon (g = 1.62 N/kg). How much does it weigh there?
- Why does an astronaut's mass not change in space, but their weight does?