Question

How do I calculate the gravitational force between two 50 kg objects separated by 2 meters using the universal gravitation formula?

Answer 1

To calculate the gravitational force between two objects using Newton's law of universal gravitation, you can use the following formula:

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

Where:
- \( F \) is the gravitational force between the two masses,
- \( G \) is the gravitational constant, approximately \( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \),
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two masses.

For your case:
- \( m_1 = 50 \, \text{kg} \)
- \( m_2 = 50 \, \text{kg} \)
- \( r = 2 \, \text{m} \)

Now, let's plug in the values into the formula:

\[
F = (6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2) \frac{(50 \, \text{kg})(50 \, \text{kg})}{(2 \, \text{m})^2}
\]

Calculating the terms step-by-step:

1. Calculate the mass product:
\[
50 \, \text{kg} \times 50 \, \text{kg} = 2500 \, \text{kg}^2
\]

2. Calculate the distance squared:
\[
(2 \, \text{m})^2 = 4 \, \text{m}^2
\]

3. Now substitute these values back into the equation:
\[
F = (6.674 \times 10^{-11}) \frac{2500}{4}
\]

4. Simplify the fraction:
\[
\frac{2500}{4} = 625
\]

5. Now calculate the force:
\[
F = (6.674 \times 10^{-11}) \times 625
\]

6. Perform the multiplication:
\[
F = 4.17125 \times 10^{-8} \, \text{N}
\]

Thus, the gravitational force between the two 50 kg objects separated by 2 meters is approximately:

\[
F \approx 4.17 \times 10^{-8} \, \text{N}
\]