Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To determine the force of gravity acting on a 1-kilogram box located [tex]\(1.3 \times 10^7\)[/tex] meters from the center of the Earth, we will use the formula for gravitational force:
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force,
- [tex]\( G \)[/tex] is the gravitational constant ([tex]\(6.673 \times 10^{-11}\)[/tex] N·m[tex]\(^2\)[/tex]/kg[tex]\(^2\)[/tex]),
- [tex]\( m_1 \)[/tex] is the mass of the Earth ([tex]\(5.98 \times 10^{24}\)[/tex] kg),
- [tex]\( m_2 \)[/tex] is the mass of the box (1 kg),
- [tex]\( r \)[/tex] is the distance from the center of the Earth ([tex]\(1.3 \times 10^7\)[/tex] m).
Let's break down the calculation:
1. Calculate the numerator [tex]\( G \cdot m_1 \cdot m_2 \)[/tex]:
[tex]\[ 6.673 \times 10^{-11} \, \text{N·m}^2/\text{kg}^2 \times 5.98 \times 10^{24} \, \text{kg} \times 1 \, \text{kg} \][/tex]
2. Calculate the denominator [tex]\( r^2 \)[/tex]:
[tex]\[ (1.3 \times 10^7 \, \text{m})^2 \][/tex]
3. Divide the numerator by the denominator to find [tex]\( F \)[/tex]:
[tex]\[ F = \frac{6.673 \times 10^{-11} \, \text{N·m}^2/\text{kg}^2 \times 5.98 \times 10^{24} \, \text{kg} \times 1 \, \text{kg}}{(1.3 \times 10^7 \, \text{m})^2} \][/tex]
Upon performing the calculations, we find that:
[tex]\[ F \approx 2.3612153846153845 \, \text{newtons} \][/tex]
Thus, the correct answer is approximately 2.36 newtons.
So, the correct answer is:
A. 2.36 newtons
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force,
- [tex]\( G \)[/tex] is the gravitational constant ([tex]\(6.673 \times 10^{-11}\)[/tex] N·m[tex]\(^2\)[/tex]/kg[tex]\(^2\)[/tex]),
- [tex]\( m_1 \)[/tex] is the mass of the Earth ([tex]\(5.98 \times 10^{24}\)[/tex] kg),
- [tex]\( m_2 \)[/tex] is the mass of the box (1 kg),
- [tex]\( r \)[/tex] is the distance from the center of the Earth ([tex]\(1.3 \times 10^7\)[/tex] m).
Let's break down the calculation:
1. Calculate the numerator [tex]\( G \cdot m_1 \cdot m_2 \)[/tex]:
[tex]\[ 6.673 \times 10^{-11} \, \text{N·m}^2/\text{kg}^2 \times 5.98 \times 10^{24} \, \text{kg} \times 1 \, \text{kg} \][/tex]
2. Calculate the denominator [tex]\( r^2 \)[/tex]:
[tex]\[ (1.3 \times 10^7 \, \text{m})^2 \][/tex]
3. Divide the numerator by the denominator to find [tex]\( F \)[/tex]:
[tex]\[ F = \frac{6.673 \times 10^{-11} \, \text{N·m}^2/\text{kg}^2 \times 5.98 \times 10^{24} \, \text{kg} \times 1 \, \text{kg}}{(1.3 \times 10^7 \, \text{m})^2} \][/tex]
Upon performing the calculations, we find that:
[tex]\[ F \approx 2.3612153846153845 \, \text{newtons} \][/tex]
Thus, the correct answer is approximately 2.36 newtons.
So, the correct answer is:
A. 2.36 newtons
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.