Take weights of five of your friends. Find out what their weights will be on the moon and the Mars.

Answer: Mass stays the same; weight \(W = mg\) on the moon is about 1/6 and on Mars about 0.38 of the weight on earth (see table).

Important: a weighing machine shows our mass in kg. Mass is the amount of matter in a body and stays the same everywhere. Weight is the gravitational force on the body, \(W = mg\), and is measured in newtons (N). So the mass of each friend is the same on the earth, the moon and Mars; only the weight changes.

Values used: \(g_{earth} = 9.8\ \text{m/s}^2\), \(g_{moon} = \tfrac{1}{6} g_{earth} \approx 1.63\ \text{m/s}^2\), \(g_{Mars} \approx 3.7\ \text{m/s}^2\) (about 0.38 times that of the earth).

Suppose the masses of five friends (as shown by the weighing machine) are 45 kg, 50 kg, 40 kg, 36 kg and 60 kg.

Example (Friend 1, \(m = 45\) kg):

Earth: \(W = 45 \times 9.8 = 441\ \text{N}\)

Moon: \(W = \tfrac{441}{6} = 73.5\ \text{N}\)

Mars: \(W = 45 \times 3.7 = 166.5\ \text{N}\)

Similarly for all five friends:

The masses (45, 50, 40, 36, 60 kg) remain the same on the moon and Mars; only the weights change. (Use your own friends' masses in the same way.)

Mass stays the same everywhere; only weight changes. Weight on the Moon = \(m \times 1.63\ \mathrm{N}\) and on Mars = \(m \times 3.7\ \mathrm{N}\), where \(m\) is the mass in kg.

A weighing machine actually shows our mass in kg. Weight is the force of gravity on that mass:

\[W = mg\]

Use \(g_{\text{Earth}} = 9.8\ \mathrm{m/s^2}\), \(g_{\text{Moon}} = \tfrac{1}{6}\times 9.8 \approx 1.63\ \mathrm{m/s^2}\) and \(g_{\text{Mars}} \approx 3.7\ \mathrm{m/s^2}\) (about 0.38 of Earth's).

Example with five friends whose masses are 40, 50, 60, 70 and 80 kg:

For example, for 70 kg: on the Moon \(W = 70 \times 1.63 \approx 114.3\ \mathrm{N}\); on Mars \(W = 70 \times 3.7 = 259\ \mathrm{N}\). The mass is still 70 kg on both. Use your own friends' masses in the same way.