Calculating Weight on the Moon

This question asks us to find a person's weight on the Moon given their weight on the Earth. To solve this, we need to understand what weight is and how gravity affects it.

Understanding Weight and Gravity

• Weight is the force of gravity acting on an object's mass.
• The formula for weight is: \( \text{Weight} = \text{mass} \times \text{acceleration due to gravity} \).
• Mass is the amount of matter in an object, and it remains constant regardless of location.
• The acceleration due to gravity varies from one celestial body to another (like Earth vs. Moon).

Gravity on the Moon compared to Earth

The acceleration due to gravity on the surface of the Moon is approximately one-sixth (\(1/6\)) of the acceleration due to gravity on the surface of the Earth. Let's denote the acceleration due to gravity on Earth as \(g_e\) and on the Moon as \(g_m\). Then, \(g_m \approx \frac{1}{6} g_e\).

Calculating Weight on the Moon

Let \(m\) be the mass of the person. The person's weight on Earth (\(W_e\)) is given by:

\( W_e = m \times g_e \)

The person's weight on the Moon (\(W_m\)) is given by:

\( W_m = m \times g_m \)

Since \(g_m \approx \frac{1}{6} g_e\), we can substitute this into the equation for \(W_m\):

\( W_m = m \times \left(\frac{1}{6} g_e\right) \)

\( W_m = \frac{1}{6} \times (m \times g_e) \)

Notice that \(m \times g_e\) is the weight on Earth, \(W_e\). So, we can write:

\( W_m = \frac{1}{6} W_e \)

The question states that the person's weight on Earth is 66 N.

Substituting the value of \(W_e\) into the equation:

\( W_m = \frac{1}{6} \times 66 \, \text{N} \)

Now, we calculate the value:

\( W_m = \frac{66}{6} \, \text{N} \)

\( W_m = 11 \, \text{N} \)

So, the person's weight on the Moon is 11 N.

Comparing with Options

Let's look at the given options:

• 55 N
• 11 N
• 132 N
• 77 N

Our calculated weight on the Moon is 11 N, which matches one of the options.

Conclusion

Based on the calculation using the relationship between gravitational acceleration on the Earth and the Moon, a person weighing 66 N on Earth would weigh 11 N on the Moon.

Revision Table: Weight and Gravity Concepts

Additional Information: Gravity and Location

The reason weight changes but mass stays the same is fundamental to physics. Gravity is a force of attraction between objects with mass. The strength of this force depends on the masses of the objects and the distance between them. Larger planets or moons have stronger gravitational pulls.

• Earth is more massive than the Moon, so Earth's gravity is stronger.
• The acceleration due to gravity on Earth is approximately 9.8 m/s².
• The acceleration due to gravity on the Moon is approximately 1.62 m/s².
• Notice that \(1.62 \, \text{m/s}^2 \approx \frac{1}{6} \times 9.8 \, \text{m/s}^2\).

This difference in gravitational acceleration directly impacts the weight of an object, even though its mass remains unchanged.