# FHSST Physics/Newtonian Gravitation/Mass and Weight

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# Mass and Weight

Weight is a force which is measured in Newtons, it is the force on an object due to gravity. People are always asking other people "What is your weight?" when a physicist might ask the same question as "What is your mass?".

Mass is measured in kilograms (kg) and is the amount of matter in an object, it doesn't change unless you add or remove matter from the object (if you continue to study physics through to university level, you will find that Einstein's theory of relativity means that mass can change when you travel as fast as light does, but you don't need to worry about that right now). There are 1000 g in 1 kg and 1000 kg in a tonne.

To change mass into weight we use Newton's 2nd Law which is $F=ma$ . The weight is the force and gravity the acceleration, it can be rewritten as:

 ${\begin{matrix}W=mg\end{matrix}}$ (9.2)

W is the weight, measured in newtons. m is the mass, measured in kilograms and g is the acceleration due to gravity, measured in metres per second squared; it is equal to about 10 on the Earth. The exact value of Earths equatorial surface gravity is 9.7801 $m.s^{-2}$ .

## Examples

1. A bag of sugar has a mass of 1 kg, what is its weight? (Acceleration due to gravity = 10 $m.s^{-2}$ )

Step 1: Always write out the equation, it helps you to understand the question, and you will get marks as well.

 ${\begin{matrix}W=mg\end{matrix}}$ (9.7)

Step 2: Fill in all the values you know. (remember to make sure the mass is in kilograms and NOT in grams or tonnes!)

 ${\begin{matrix}W=1\times 10\end{matrix}}$ $W=10$ (9.8)

Step 3: Write out the answer remembering to include the units! You will lose marks if you don't

 ${\begin{matrix}W=10\ newtons\end{matrix}}$ (9.9)

2. A space-man has a mass of 90 kg, what is his weight (a) on the earth? (b) on the moon? (c) in outer space? (The acceleration due to gravity on the earth is 10 $m.s^{-2}$ , on the moon gravity is about 1/6 of the gravity on earth).

1:

 ${\begin{matrix}W=mg\end{matrix}}$ ${\begin{matrix}W=90\times 10=900\end{matrix}}$ $W=900\ newtons$ (9.10)

2:

 $W=M\ g$ ${\begin{matrix}W=90\times \ 10\times {\frac {1}{6}}=150\end{matrix}}$ $W=150\ newtons$ (9.10)

3: Weightless in outer space because g = 0.

So now when somebody asks you your weight, you know to reply Anything!! But my mass is a different matter!"