Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To determine the gravitational force between the semitruck and the car, we'll use Newton's law of universal gravitation. The formula for the gravitational force [tex]\( F \)[/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 semitruck, [tex]\( 20{,}000 \, \text{kg} \)[/tex],
- [tex]\( m_2 \)[/tex] is the mass of the car, [tex]\( 2{,}000 \, \text{kg} \)[/tex],
- [tex]\( r \)[/tex] is the distance between the semitruck and the car, [tex]\( 10 \, \text{m} \)[/tex].
Let's plug in the given values into the formula:
1. Calculate the product of the masses:
[tex]\[ m_1 \cdot m_2 = 20{,}000 \, \text{kg} \times 2{,}000 \, \text{kg} = 40{,}000{,}000 \, \text{kg}^2 \][/tex]
2. Calculate the square of the distance:
[tex]\[ r^2 = (10 \, \text{m})^2 = 100 \, \text{m}^2 \][/tex]
3. Plug these values and [tex]\( G \)[/tex] into the formula:
[tex]\[ F = 6.67 \times 10^{-11} \cdot \frac{40{,}000{,}000}{100} \][/tex]
4. Simplify the fraction:
[tex]\[ \frac{40{,}000{,}000}{100} = 400{,}000 \][/tex]
5. Multiply by the gravitational constant [tex]\( G \)[/tex]:
[tex]\[ F = 6.67 \times 10^{-11} \cdot 400{,}000 \][/tex]
[tex]\[ F = 2.668 \times 10^{-5} \, \text{N} \][/tex]
Thus, the gravitational force between the semitruck and the car is approximately [tex]\( 2.67 \times 10^{-5} \, \text{N} \)[/tex].
Therefore, the correct answer is:
C. [tex]\( 2.67 \times 10^{-5} \, \text{N} \)[/tex]
[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 semitruck, [tex]\( 20{,}000 \, \text{kg} \)[/tex],
- [tex]\( m_2 \)[/tex] is the mass of the car, [tex]\( 2{,}000 \, \text{kg} \)[/tex],
- [tex]\( r \)[/tex] is the distance between the semitruck and the car, [tex]\( 10 \, \text{m} \)[/tex].
Let's plug in the given values into the formula:
1. Calculate the product of the masses:
[tex]\[ m_1 \cdot m_2 = 20{,}000 \, \text{kg} \times 2{,}000 \, \text{kg} = 40{,}000{,}000 \, \text{kg}^2 \][/tex]
2. Calculate the square of the distance:
[tex]\[ r^2 = (10 \, \text{m})^2 = 100 \, \text{m}^2 \][/tex]
3. Plug these values and [tex]\( G \)[/tex] into the formula:
[tex]\[ F = 6.67 \times 10^{-11} \cdot \frac{40{,}000{,}000}{100} \][/tex]
4. Simplify the fraction:
[tex]\[ \frac{40{,}000{,}000}{100} = 400{,}000 \][/tex]
5. Multiply by the gravitational constant [tex]\( G \)[/tex]:
[tex]\[ F = 6.67 \times 10^{-11} \cdot 400{,}000 \][/tex]
[tex]\[ F = 2.668 \times 10^{-5} \, \text{N} \][/tex]
Thus, the gravitational force between the semitruck and the car is approximately [tex]\( 2.67 \times 10^{-5} \, \text{N} \)[/tex].
Therefore, the correct answer is:
C. [tex]\( 2.67 \times 10^{-5} \, \text{N} \)[/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.