Question

Two spherical objects have masses of 220kg and 580kg.Their centers are separated by a distance of 10 meters. Find the gravitational attraction between them in Newtons.

Answer 1

To find the gravitational attraction between two spherical objects, we can use Newton's law of universal gravitation, which states:

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

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

Given:
- \( m_1 = 220 \, \text{kg} \)
- \( m_2 = 580 \, \text{kg} \)
- \( r = 10 \, \text{m} \)

Substituting in the values:

\[
F = \frac{6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \cdot 220 \, \text{kg} \cdot 580 \, \text{kg}}{(10 \, \text{m})^2}
\]

Calculating the mass product:

\[
220 \, \text{kg} \cdot 580 \, \text{kg} = 127600 \, \text{kg}^2
\]

Calculating the square of the distance:

\[
(10 \, \text{m})^2 = 100 \, \text{m}^2
\]

Now substituting back into the equation:

\[
F = \frac{6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \cdot 127600 \, \text{kg}^2}{100 \, \text{m}^2}
\]

Calculating:

\[
F = \frac{6.674 \times 10^{-11} \cdot 127600}{100}
\]

Calculating \( 6.674 \times 127600 \):

\[
6.674 \times 127600 \approx 8516064.4
\]

Now divide by 100:

\[
F \approx \frac{8516064.4}{100} = 85160.644 \, \text{N}
\]

Thus, the gravitational attraction between the two spherical objects is approximately:

\[
\boxed{85160.64 \, \text{N}}
\]