Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To find the gravitational force between two objects, you can use Newton's law of universal gravitation. The formula is:
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force between the two 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 two objects (in kilograms),
- [tex]\( r \)[/tex] is the distance between the centers of the two objects (in meters).
Given:
- The mass of each bowling ball, [tex]\( m_1 = m_2 = 8 \, \text{kg} \)[/tex],
- The distance between the two bowling balls, [tex]\( r = 2 \, \text{m} \)[/tex].
Now plug these values into the formula:
[tex]\[ F = \left( 6.67 \times 10^{-11} \, \text{N} \cdot \left(\text{m}^2 / \text{kg}^2\right) \right) \frac{8 \, \text{kg} \times 8 \, \text{kg}}{(2 \, \text{m})^2} \][/tex]
First, calculate [tex]\( (2 \, \text{m})^2 \)[/tex]:
[tex]\[ (2 \, \text{m})^2 = 4 \, \text{m}^2 \][/tex]
Next, calculate [tex]\( 8 \, \text{kg} \times 8 \, \text{kg} \)[/tex]:
[tex]\[ 8 \, \text{kg} \times 8 \, \text{kg} = 64 \, \text{kg}^2 \][/tex]
Now the formula looks like this:
[tex]\[ F = \left( 6.67 \times 10^{-11} \, \text{N} \cdot (\text{m}^2 / \text{kg}^2) \right) \frac{64 \, \text{kg}^2}{4 \, \text{m}^2} \][/tex]
Divide [tex]\( 64 \, \text{kg}^2 \)[/tex] by [tex]\( 4 \, \text{m}^2 \)[/tex]:
[tex]\[ \frac{64 \, \text{kg}^2}{4 \, \text{m}^2} = 16 \, \text{kg}^2 / \text{m}^2 \][/tex]
Now multiply:
[tex]\[ F = 6.67 \times 10^{-11} \, \text{N} \cdot (\text{m}^2 / \text{kg}^2) \times 16 \, \text{kg}^2 / \text{m}^2 \][/tex]
[tex]\[ F = 6.67 \times 10^{-11} \times 16 \][/tex]
Calculate [tex]\( 6.67 \times 16 \)[/tex]:
[tex]\[ 6.67 \times 16 = 106.72 \][/tex]
Now add the exponent:
[tex]\[ 106.72 \times 10^{-11} = 1.0672 \times 10^{-9} \, \text{N} \][/tex]
So, the gravitational force between the two bowling balls is:
[tex]\[ F = 1.0672 \times 10^{-9} \, \text{N} \][/tex]
Referring to the given options:
- A. [tex]\( 2.14 \times 10^{-9} \, \text{N} \)[/tex]
- B. [tex]\( 3.21 \times 10^{-8} \, \text{N} \)[/tex]
- C. [tex]\( 2.68 \times 10^{-10} \, \text{N} \)[/tex]
- D. [tex]\( 1.07 \times 10^{-9} \, \text{N} \)[/tex]
The closest and correct answer is:
D. [tex]\( 1.07 \times 10^{-9} \, \text{N} \)[/tex]
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force between the two 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 two objects (in kilograms),
- [tex]\( r \)[/tex] is the distance between the centers of the two objects (in meters).
Given:
- The mass of each bowling ball, [tex]\( m_1 = m_2 = 8 \, \text{kg} \)[/tex],
- The distance between the two bowling balls, [tex]\( r = 2 \, \text{m} \)[/tex].
Now plug these values into the formula:
[tex]\[ F = \left( 6.67 \times 10^{-11} \, \text{N} \cdot \left(\text{m}^2 / \text{kg}^2\right) \right) \frac{8 \, \text{kg} \times 8 \, \text{kg}}{(2 \, \text{m})^2} \][/tex]
First, calculate [tex]\( (2 \, \text{m})^2 \)[/tex]:
[tex]\[ (2 \, \text{m})^2 = 4 \, \text{m}^2 \][/tex]
Next, calculate [tex]\( 8 \, \text{kg} \times 8 \, \text{kg} \)[/tex]:
[tex]\[ 8 \, \text{kg} \times 8 \, \text{kg} = 64 \, \text{kg}^2 \][/tex]
Now the formula looks like this:
[tex]\[ F = \left( 6.67 \times 10^{-11} \, \text{N} \cdot (\text{m}^2 / \text{kg}^2) \right) \frac{64 \, \text{kg}^2}{4 \, \text{m}^2} \][/tex]
Divide [tex]\( 64 \, \text{kg}^2 \)[/tex] by [tex]\( 4 \, \text{m}^2 \)[/tex]:
[tex]\[ \frac{64 \, \text{kg}^2}{4 \, \text{m}^2} = 16 \, \text{kg}^2 / \text{m}^2 \][/tex]
Now multiply:
[tex]\[ F = 6.67 \times 10^{-11} \, \text{N} \cdot (\text{m}^2 / \text{kg}^2) \times 16 \, \text{kg}^2 / \text{m}^2 \][/tex]
[tex]\[ F = 6.67 \times 10^{-11} \times 16 \][/tex]
Calculate [tex]\( 6.67 \times 16 \)[/tex]:
[tex]\[ 6.67 \times 16 = 106.72 \][/tex]
Now add the exponent:
[tex]\[ 106.72 \times 10^{-11} = 1.0672 \times 10^{-9} \, \text{N} \][/tex]
So, the gravitational force between the two bowling balls is:
[tex]\[ F = 1.0672 \times 10^{-9} \, \text{N} \][/tex]
Referring to the given options:
- A. [tex]\( 2.14 \times 10^{-9} \, \text{N} \)[/tex]
- B. [tex]\( 3.21 \times 10^{-8} \, \text{N} \)[/tex]
- C. [tex]\( 2.68 \times 10^{-10} \, \text{N} \)[/tex]
- D. [tex]\( 1.07 \times 10^{-9} \, \text{N} \)[/tex]
The closest and correct answer is:
D. [tex]\( 1.07 \times 10^{-9} \, \text{N} \)[/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
