At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Sure, let's solve this step-by-step.
The gravitational force between two objects can be calculated using Newton's law of universal gravitation, which is given by the formula:
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
Where:
- [tex]\( F \)[/tex] is the gravitational force between the objects
- [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] and [tex]\( m_2 \)[/tex] are the masses of the objects
- [tex]\( r \)[/tex] is the distance between the centers of the two masses
Here we have:
- [tex]\( m_1 = 0.1 \, \text{kg} \)[/tex]
- [tex]\( m_2 = 0.1 \, \text{kg} \)[/tex]
- [tex]\( r = 0.15 \, \text{m} \)[/tex]
Step-by-step solution:
1. We need to substitute the given values into the formula.
2. The formula becomes:
[tex]\[ F = 6.67 \times 10^{-11} \, \text{N} \cdot \frac{(0.1 \, \text{kg}) \cdot (0.1 \, \text{kg})}{(0.15 \, \text{m})^2} \][/tex]
3. First, calculate the product of the masses:
[tex]\[ 0.1 \, \text{kg} \times 0.1 \, \text{kg} = 0.01 \, \text{kg}^2 \][/tex]
4. Next, calculate the square of the distance:
[tex]\[ (0.15 \, \text{m})^2 = 0.0225 \, \text{m}^2 \][/tex]
5. Now, substitute these values back into the formula:
[tex]\[ F = 6.67 \times 10^{-11} \, \frac{0.01 \, \text{kg}^2}{0.0225 \, \text{m}^2} \][/tex]
6. Simplify the fraction:
[tex]\[ F = 6.67 \times 10^{-11} \times \frac{0.01}{0.0225} \][/tex]
[tex]\[ F = 6.67 \times 10^{-11} \times 0.4444 \][/tex]
7. Finally, multiply the values:
[tex]\[ F \approx 2.9644 \times 10^{-11} \, \text{N} \][/tex]
Thus, the gravitational force between the shoes is approximately [tex]\( 2.9644 \times 10^{-11} \, \text{N} \)[/tex].
Among the given choices:
A. [tex]\( 2.96 \times 10^{-10} \, \text{N} \)[/tex]
B. [tex]\( 296 \times 10^{-11} \, \text{N} \)[/tex]
C. [tex]\( 4.44 \times 10^{-11} \, \text{N} \)[/tex]
D. [tex]\( 4.44 \times 10^{-12} \, \text{N} \)[/tex]
The correct answer is not exactly listed among the choices, but the closest one, considering significant figures and rounding, would be:
B. [tex]\( 296 \times 10^{-11} \, \text{N} \)[/tex]
This is equivalent to [tex]\( 2.96 \times 10^{-10} \, \text{N} \)[/tex] when rewritten in standard form.
The gravitational force between two objects can be calculated using Newton's law of universal gravitation, which is given by the formula:
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
Where:
- [tex]\( F \)[/tex] is the gravitational force between the objects
- [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] and [tex]\( m_2 \)[/tex] are the masses of the objects
- [tex]\( r \)[/tex] is the distance between the centers of the two masses
Here we have:
- [tex]\( m_1 = 0.1 \, \text{kg} \)[/tex]
- [tex]\( m_2 = 0.1 \, \text{kg} \)[/tex]
- [tex]\( r = 0.15 \, \text{m} \)[/tex]
Step-by-step solution:
1. We need to substitute the given values into the formula.
2. The formula becomes:
[tex]\[ F = 6.67 \times 10^{-11} \, \text{N} \cdot \frac{(0.1 \, \text{kg}) \cdot (0.1 \, \text{kg})}{(0.15 \, \text{m})^2} \][/tex]
3. First, calculate the product of the masses:
[tex]\[ 0.1 \, \text{kg} \times 0.1 \, \text{kg} = 0.01 \, \text{kg}^2 \][/tex]
4. Next, calculate the square of the distance:
[tex]\[ (0.15 \, \text{m})^2 = 0.0225 \, \text{m}^2 \][/tex]
5. Now, substitute these values back into the formula:
[tex]\[ F = 6.67 \times 10^{-11} \, \frac{0.01 \, \text{kg}^2}{0.0225 \, \text{m}^2} \][/tex]
6. Simplify the fraction:
[tex]\[ F = 6.67 \times 10^{-11} \times \frac{0.01}{0.0225} \][/tex]
[tex]\[ F = 6.67 \times 10^{-11} \times 0.4444 \][/tex]
7. Finally, multiply the values:
[tex]\[ F \approx 2.9644 \times 10^{-11} \, \text{N} \][/tex]
Thus, the gravitational force between the shoes is approximately [tex]\( 2.9644 \times 10^{-11} \, \text{N} \)[/tex].
Among the given choices:
A. [tex]\( 2.96 \times 10^{-10} \, \text{N} \)[/tex]
B. [tex]\( 296 \times 10^{-11} \, \text{N} \)[/tex]
C. [tex]\( 4.44 \times 10^{-11} \, \text{N} \)[/tex]
D. [tex]\( 4.44 \times 10^{-12} \, \text{N} \)[/tex]
The correct answer is not exactly listed among the choices, but the closest one, considering significant figures and rounding, would be:
B. [tex]\( 296 \times 10^{-11} \, \text{N} \)[/tex]
This is equivalent to [tex]\( 2.96 \times 10^{-10} \, \text{N} \)[/tex] when rewritten in standard form.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.