Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To calculate the force of gravity between the two spaceships, we will use Newton's law of universal gravitation, which states that the gravitational force [tex]\( F \)[/tex] between two masses [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] separated by a distance [tex]\( r \)[/tex] is given by:
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
where:
- [tex]\( G \)[/tex] is the gravitational constant, [tex]\( 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \)[/tex],
- [tex]\( m_1 \)[/tex] is the mass of the first spaceship, [tex]\( 300,000 \, \text{kg} \)[/tex],
- [tex]\( m_2 \)[/tex] is the mass of the second spaceship, [tex]\( 300,000 \, \text{kg} \)[/tex],
- [tex]\( r \)[/tex] is the distance between the two spaceships, [tex]\( 250 \, \text{m} \)[/tex].
Following these steps:
1. Substitute the given values into the formula:
[tex]\[ F = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \times \frac{300,000 \, \text{kg} \times 300,000 \, \text{kg}}{(250 \, \text{m})^2} \][/tex]
2. Calculate the product of the masses:
[tex]\[ 300,000 \times 300,000 = 90,000,000,000 \, \text{kg}^2 \][/tex]
3. Calculate the square of the distance:
[tex]\[ (250 \, \text{m})^2 = 62,500 \, \text{m}^2 \][/tex]
4. Substitute these results back into the formula:
[tex]\[ F = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \times \frac{90,000,000,000 \, \text{kg}^2}{62,500 \, \text{m}^2} \][/tex]
5. Perform the division in the fraction:
[tex]\[ \frac{90,000,000,000}{62,500} = 1,440,000 \][/tex]
6. Multiply by the gravitational constant:
[tex]\[ F = 6.67 \times 10^{-11} \times 1,440,000 \, \text{N} \][/tex]
7. Calculate the final result:
[tex]\[ F \approx 9.6048 \times 10^{-5} \, \text{N} \][/tex]
Therefore, the force of gravity between the two spaceships is [tex]\( 9.6 \times 10^{-5} \)[/tex] N, which corresponds to option B.
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
where:
- [tex]\( G \)[/tex] is the gravitational constant, [tex]\( 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \)[/tex],
- [tex]\( m_1 \)[/tex] is the mass of the first spaceship, [tex]\( 300,000 \, \text{kg} \)[/tex],
- [tex]\( m_2 \)[/tex] is the mass of the second spaceship, [tex]\( 300,000 \, \text{kg} \)[/tex],
- [tex]\( r \)[/tex] is the distance between the two spaceships, [tex]\( 250 \, \text{m} \)[/tex].
Following these steps:
1. Substitute the given values into the formula:
[tex]\[ F = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \times \frac{300,000 \, \text{kg} \times 300,000 \, \text{kg}}{(250 \, \text{m})^2} \][/tex]
2. Calculate the product of the masses:
[tex]\[ 300,000 \times 300,000 = 90,000,000,000 \, \text{kg}^2 \][/tex]
3. Calculate the square of the distance:
[tex]\[ (250 \, \text{m})^2 = 62,500 \, \text{m}^2 \][/tex]
4. Substitute these results back into the formula:
[tex]\[ F = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \times \frac{90,000,000,000 \, \text{kg}^2}{62,500 \, \text{m}^2} \][/tex]
5. Perform the division in the fraction:
[tex]\[ \frac{90,000,000,000}{62,500} = 1,440,000 \][/tex]
6. Multiply by the gravitational constant:
[tex]\[ F = 6.67 \times 10^{-11} \times 1,440,000 \, \text{N} \][/tex]
7. Calculate the final result:
[tex]\[ F \approx 9.6048 \times 10^{-5} \, \text{N} \][/tex]
Therefore, the force of gravity between the two spaceships is [tex]\( 9.6 \times 10^{-5} \)[/tex] N, which corresponds to option B.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.