\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \tau{\uptau}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\) \(\def \ccw{\circlearrowleft}\) \(\def \cw{\circlearrowright}\)

Chapter 1: Equilibrium

20. (Problem Solving)

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

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.