Changing Between Mass and Weight

Telling the difference between mass and weight:

• Mass has units of kilograms (or maybe grams), while weight has units of Newtons.
• Weight is a force, and so might appear with other forces.
• Weight is a vector quantity, and so has a direction (usually down on Earth).
• Mass is the same everywhere; weight changes depending on what planet you are on or near.

How to convert between them:

• $W=mg$, where $g=9.8\mathrm{N}/\mathrm{kg}$ on Earth. (You can round that off to 10 for quick mental calculations, but not in homework.)
• Example: A $5\mathrm{kg}$ mass has a weight of $(5\cancel{\mathrm{kg}})(9.8\mathrm{N}/\cancel{\mathrm{kg}})=49\mathrm{N}$
• Example: An object with a weight of $10\mathrm{N}$ has a mass of $\frac{10\cancel{\mathrm{N}}}{9.8\cancel{\mathrm{N}}/\mathrm{kg}}=1.02\mathrm{kg}$

Hints:

• On Earth, weight in N is always about ten times larger than mass, and is noticeably larger. (e.g. 5kg and 49N, 1.02kg and 10N)
• The units of $g$ can also help you remember whether to multiple or divide.