Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To find the gravitational force between a baseball and a bowling ball when their centers are 0.5 meters apart, we use Newton's law of universal gravitation. The formula for 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:
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
where:
- [tex]\( G \)[/tex] is the gravitational constant, [tex]\(6.67430 \times 10^{-11} \text{ m}^3 \text{ kg}^{-1} \text{ s}^{-2} \)[/tex],
- [tex]\( m_1 \)[/tex] is the mass of the first object (the baseball), [tex]\(0.145 \text{ kg} \)[/tex],
- [tex]\( m_2 \)[/tex] is the mass of the second object (the bowling ball), [tex]\(6.8 \text{ kg} \)[/tex],
- [tex]\( r \)[/tex] is the distance between the centers of the two objects, [tex]\(0.5 \text{ m} \)[/tex].
Using these values, we substitute into the formula:
[tex]\[ F = 6.67430 \times 10^{-11} \frac{(0.145 \times 6.8)}{(0.5)^2} \][/tex]
First, calculate the numerator:
[tex]\[ 0.145 \times 6.8 = 0.986 \][/tex]
Next, calculate the square of the distance:
[tex]\[ 0.5^2 = 0.25 \][/tex]
Then, divide the product of the masses by the square of the distance:
[tex]\[ \frac{0.986}{0.25} = 3.944 \][/tex]
Now, multiply by the gravitational constant:
[tex]\[ F = 6.67430 \times 10^{-11} \times 3.944 = 2.63234392 \times 10^{-10} \text{ N} \][/tex]
Therefore, the gravitational force between the baseball and the bowling ball is approximately:
[tex]\[ 2.63234392 \times 10^{-10} \text{ N} \][/tex]
Matching this result with the given choices, the closest answer is:
[tex]\[ 2.6 \times 10^{-10} \text{ N} \][/tex]
Thus, the correct answer is:
[tex]\[ 2.6 \times 10^{-10} \text{ N} \][/tex]
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
where:
- [tex]\( G \)[/tex] is the gravitational constant, [tex]\(6.67430 \times 10^{-11} \text{ m}^3 \text{ kg}^{-1} \text{ s}^{-2} \)[/tex],
- [tex]\( m_1 \)[/tex] is the mass of the first object (the baseball), [tex]\(0.145 \text{ kg} \)[/tex],
- [tex]\( m_2 \)[/tex] is the mass of the second object (the bowling ball), [tex]\(6.8 \text{ kg} \)[/tex],
- [tex]\( r \)[/tex] is the distance between the centers of the two objects, [tex]\(0.5 \text{ m} \)[/tex].
Using these values, we substitute into the formula:
[tex]\[ F = 6.67430 \times 10^{-11} \frac{(0.145 \times 6.8)}{(0.5)^2} \][/tex]
First, calculate the numerator:
[tex]\[ 0.145 \times 6.8 = 0.986 \][/tex]
Next, calculate the square of the distance:
[tex]\[ 0.5^2 = 0.25 \][/tex]
Then, divide the product of the masses by the square of the distance:
[tex]\[ \frac{0.986}{0.25} = 3.944 \][/tex]
Now, multiply by the gravitational constant:
[tex]\[ F = 6.67430 \times 10^{-11} \times 3.944 = 2.63234392 \times 10^{-10} \text{ N} \][/tex]
Therefore, the gravitational force between the baseball and the bowling ball is approximately:
[tex]\[ 2.63234392 \times 10^{-10} \text{ N} \][/tex]
Matching this result with the given choices, the closest answer is:
[tex]\[ 2.6 \times 10^{-10} \text{ N} \][/tex]
Thus, the correct answer is:
[tex]\[ 2.6 \times 10^{-10} \text{ N} \][/tex]
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 this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.