In everyday talk, "mass" and "weight" mean the same thing. In physics they don't. Your mass is the amount of matter in you, in kilograms. Your weight is a force: the pull of gravity on that mass, in newtons. It follows from the second law.
Key idea
Weight $W = m\,g$. Near Earth's surface $g = 9.8\,\mathrm{N/kg}$, so each kilogram weighs 9.8 N. Mass is the same everywhere; weight depends on where you are.
Why it works
Drop anything and it falls with acceleration $g = 9.8\,\mathrm{m/s^2}$. By $F = ma$, the force that causes this is $m \times 9.8$, and that force is the weight. On the Moon, gravity is weaker ($g \approx 1.6\,\mathrm{N/kg}$), so the same mass weighs about one sixth as much. The astronaut is not smaller; the Moon just pulls less.
Worked example: Weight on Earth
Find the weight of a 50 kg student on Earth.
- $W = m\,g = 50\,\mathrm{kg} \times 9.8\,\mathrm{N/kg}$.
- $W = 490\,\mathrm{N}$.
Answer: $490\,\mathrm{N}$
Worked example: The same student on the Moon
On the Moon, $g = 1.6\,\mathrm{N/kg}$. Find the student's mass and weight there.
- Mass does not change: still $50\,\mathrm{kg}$.
- Weight: $W = 50 \times 1.6 = 80\,\mathrm{N}$.
Answer: Mass 50 kg; weight 80 N
Common mistake
Saying an astronaut's mass changes on the Moon, or giving weight in kilograms. Mass stays the same; only the weight changes. And a weight is a force, so it is in newtons. (A bathroom scale shows kilograms only because it assumes you are on Earth.) Check the unit: kg means mass, N means weight.
| Place | g (N/kg) | Weight of 10 kg |
|---|---|---|
| Earth | 9.8 | 98 N |
| Moon | 1.6 | 16 N |
| Mars | 3.7 | 37 N |
| Jupiter (cloud tops) | 24.8 | 248 N |