Compare the force of gravity on a 1 kg mass on the Moon’s surface with the force that mass on Earth’s surface. Which force is greater, why, and by how much?

To compare the force of gravity on a 1 kg mass on the Moon’s surface with the force on Earth’s surface, we'll use Newton's second law of motion, which defines the gravitational force as:

\[
F = m \cdot g
\]

Where:
- \( F \) is the force,
- \( m \) is the mass (1 kg in this case),
- \( g \) is the gravitational acceleration.

### 1. Gravitational Force on Earth
On Earth, the acceleration due to gravity (\( g_{\text{Earth}} \)) is approximately:

\[
g_{\text{Earth}} = 9.8 \, \text{m/s}^2
\]

So, the force of gravity on Earth for a 1 kg mass is:

\[
F_{\text{Earth}} = 1 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 9.8 \, \text{N}
\]

### 2. Gravitational Force on the Moon
The acceleration due to gravity on the Moon (\( g_{\text{Moon}} \)) is about:

\[
g_{\text{Moon}} = 1.625 \, \text{m/s}^2
\]

Thus, the force of gravity on the Moon for the same 1 kg mass is:

\[
F_{\text{Moon}} = 1 \, \text{kg} \times 1.625 \, \text{m/s}^2 = 1.625 \, \text{N}
\]

### 3. Comparison
The gravitational force on Earth is clearly greater than the gravitational force on the Moon.

To find how much greater the force on Earth is compared to the Moon, we can divide the force on Earth by the force on the Moon:

\[
\text{Factor increase} = \frac{F_{\text{Earth}}}{F_{\text{Moon}}} = \frac{9.8}{1.625} \approx 6.03
\]

### Conclusion
The force of gravity on a 1 kg mass on Earth is about **6 times greater** than on the Moon. This difference arises because Earth has a much larger mass and gravitational pull than the Moon.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What is the formula for gravitational force between two masses?
2. How does gravitational acceleration vary with altitude?
3. What is the escape velocity from the surface of the Moon?
4. How does the mass of an object affect its weight on different planets?
5. How would the force of gravity change on a planet with double the mass of Earth?

**Tip:** Weight and mass are often confused. Mass is constant, but weight changes depending on the gravitational field strength.

Compare the gravitational force on a 1 kg mass on the Moon and Earth. Using Newton's Second Law (F = m ⋅ g), this problem shows how Earth's gravity is about 6 times greater than the Moon's due to Earth's larger mass and gravitational pull. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation