Astronauts in training often fly in the KC-135 training aircraft to experience near-weightlessness. Three Japan Aerospace Exploration Agency astronauts—Akihiko Hoshide, Satoshi Furukawa, and Naoko Yamazaki—are shown here during such an exercise. Though they experience near-weightlessness, we can see that their mass has not changed. What is the relationship between mass and weight?

### Mass and Weight

The **mass** of an object is defined as the amount of matter in the object. The amount of mass an object has does not change; a moon rock that has been returned to Earth has the same mass on the Earth’s surface as it had on the moon. The amount of mass in an object is measured by comparing the object to known masses on an instrument called a balance.

Using the balance shown here, the object would be placed in one pan and known masses would be placed in the other pan until the pans were exactly balanced. When balanced, the mass of the object would be equal to the sum of the known masses in the other pan. A balance will work in any location; whether on the moon or on Earth, the moon rock mentioned earlier will have the same mass.

The **weight** of an object is the force pulling the object downward. On Earth, this would be the gravitational force of the Earth on the object. On the moon, this would be the gravitational force of the moon on the object. The gravitational force of the moon is one-sixth the magnitude of the gravitational force of the Earth; the weight of the moon rock on the moon will be one-sixth the weight of the moon rock on the Earth’s surface. Weight is measured in force units—newtons—by a calibrated spring scale as shown here.

The force of gravity is given by Newton’s Second Law, \begin{align*}F = ma\end{align*}, where \begin{align*}F\end{align*} is the force of gravity in newtons, \begin{align*}m\end{align*} is the mass of the object in kilograms, and \begin{align*}a\end{align*} is the acceleration due to gravity, 9.81 m/s^{2}. When the formula is used specifically for finding weight from mass or vice versa, it may appear as ** \begin{align*}W = mg\end{align*}**.

**Example Problem:** What is the weight of an object sitting on the Earth’s surface if the mass of the object is 43.7 kg?

**Solution:** \begin{align*}W = mg = (43.7 \ \text{kg})(9.81 \ \text{m/s}^2) = 429 \ \text{N}\end{align*}

**Example Problem:** What is the mass of an object whose weight sitting on the Earth is 2570 N?

\begin{align*}m=\frac{W}{a}=\frac{2570 \ \text{N}}{9.81 \ \text{m/s}^2}=262 \ \text{kg}\end{align*}

#### Summary

- The mass of an object is measured in kilograms and is defined as the amount of matter in an object.
- Mass is determined by comparing an object to known masses on a balance.
- The weight of an object on the Earth is defined as the force acting on the object by the Earth’s gravity.
- Weight is measured by a calibrated spring scale.
- The formula relating mass and weight is \begin{align*}W = mg\end{align*}.

#### Practice

*Questions*

A song about the difference between mass and weight sung by Mr. Edmunds to the tune of Sweet Caroline. Remember to make allowances for the fact that he is a teacher, not a professional singer. Use this resource to answer the questions that follow.

http://www.youtube.com/watch?v=1whMAIGNq7E

- What is used to measure mass?
- What is used to measure weight?
- What units are used to measure mass?
- What units are used to measure weight?

#### Review

*Questions*

- The mass of an object on the Earth is 100. kg.
- What is the weight of the object on the Earth?
- What is the mass of the object on the moon?
- Assuming the acceleration due to gravity on the moon is exactly one-sixth of the acceleration due to gravity on Earth, what is the weight of the object on the moon?

- A man standing on the Earth can exert the same force with his legs as when he is standing on the moon. We know that the mass of the man is the same on the Earth and the moon. We also know that \begin{align*}F = ma\end{align*} is true on both the Earth and the moon. Will the man be able to jump higher on the moon than the Earth? Why or why not?