Determine the gravitational force that you exert on another person 2.00 m away. Assume that you and the other person are point masses of 68.0 kg each.

To determine the gravitational force between two point masses, we use Newton's law of universal gravitation. The formula for the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by:

\[
F = G \frac{m_1 m_2}{r^2}
\]

where:
- \( G \) is the gravitational constant, approximately \( 6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2} \),
- \( m_1 \) and \( m_2 \) are the masses of the two objects, and
- \( r \) is the distance between the centers of the two masses.

Given:
- \( m_1 = 68.0 \, \text{kg} \)
- \( m_2 = 68.0 \, \text{kg} \)
- \( r = 2.00 \, \text{m} \)

Let's calculate the gravitational force:

\[
F = G \frac{m_1 m_2}{r^2}
\]

\[
F = (6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}) \frac{(68.0 \, \text{kg}) (68.0 \, \text{kg})}{(2.00 \, \text{m})^2}
\]

Now, let's compute the result.The gravitational force between the two people is approximately \( 7.72 \times 10^{-8} \, \text{N} \). This force is extremely small, illustrating how weak gravitational attraction is between objects of ordinary mass at relatively small distances.

Would you like more details on this calculation or have any other questions? Here are some related questions to expand on this topic:

1. How does the gravitational force change if the distance between the two people doubles?
2. What would the gravitational force be if one person's mass was doubled?
3. How does the gravitational force between two people compare to the gravitational force between the Earth and the Moon?
4. What is the gravitational force between two objects in deep space, far from any other massive bodies?
5. How does the gravitational force affect objects in everyday life?
6. What is the effect of gravitational force on larger celestial bodies, like planets or stars?
7. How would the gravitational force change if the masses of the two people were 100 kg each?
8. How does gravitational force relate to the weight of an object?

**Tip:** Gravitational force decreases with the square of the distance between two objects. Doubling the distance will decrease the force by a factor of four.

Learn how to calculate the gravitational force between two point masses using Newton's Law of Universal Gravitation. This problem involves two point masses of 68.0 kg each, separated by a distance of 2.00 m. Get a detailed solution with step-by-step calculations and explanations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation