Question

Calculate the magnitude of the gravitational force between Building X and Building Y, using the following information. a. Building X has a mass of exactly 8*10⁶ kg. b. Building Y has a mass of exactly 6*10⁷ kg. c. Their centers are located exactly 2,000m apart?

Answer 1

Magnitude of the gravitational force between Building X and Building Y is approximately
`\(8 * 10^(-15) \, \text{N}\).`

Step-by-step explanation:

The gravitational force F between two masses can be calculated using Newton's law of gravitation:

• 
  `\[ F = (G \cdot m_1 \cdot m_2)/(r^2) \]`

where:

• F is the gravitational force,
• G is the gravitational constant
  `(\( G \approx 6.674 * 10^(-11) \, \text{Nm}^2/\text{kg}^2 \)),`
• 
  `\( m_1 \)` and
  `\( m_2 \)` are the masses of the two objects,
• r is the separation between the centers of the masses.

Given that:

• 
  `\( m_1 = 8 * 10^6 \, \text{kg} \),`
• 
  `\( m_2 = 6 * 10^7 \, \text{kg} \),`
• 
  `\( r = 2000 \, \text{m} \),`

we can substitute these values into the formula:

`\[ F = \frac{(6.674 * 10^(-11) \, \text{Nm}^2/\text{kg}^2) \cdot (8 * 10^6 \, \text{kg}) \cdot (6 * 10^7 \, \text{kg})}{(2000 \, \text{m})^2} \]`

Now, calculate the force:

`\[ F \approx ((6.674 * 10^(-11)) \cdot (48 * 10^(13)))/(4 * 10^6) \]`

`\[ F \approx (320 * 10^2 * 10^(-11))/(4 * 10^6) \]`

`\[ F \approx (80 * 10^(-9))/(10^6) \]`

`\[ F \approx 8 * 10^(-15) \, \text{N} \]`

Therefore, the magnitude of the gravitational force between Building X and Building Y is approximately
`\(8 * 10^(-15) \, \text{N}\).`