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Calculate the gravitational force between two cars 5 m apart. One car has a mass of 2,565 kg and the other car has a mass of 4,264 kg. Use Newton's law of gravitation:

[tex]\[ F_{\text{gravity}} = \frac{G m_1 m_2}{r^2} \][/tex]

The gravitational constant [tex]\( G \)[/tex] is [tex]\( 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \)[/tex].

A. [tex]\( 5.84 \times 10^{-6} \, \text{N} \)[/tex]
B. [tex]\( 2.92 \times 10^{-5} \, \text{N} \)[/tex]
C. [tex]\( 4.37 \times 10^5 \, \text{N} \)[/tex]
D. [tex]\( 1.46 \times 10^{-4} \, \text{N} \)[/tex]

Sagot :

To find the gravitational force between the two cars, we use Newton's law of gravitation. The formula is given by:

[tex]\[ F_{\text{gravity}} = \frac{G m_1 m_2}{r^2} \][/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 first car, [tex]\( 2565 \, \text{kg} \)[/tex]
- [tex]\( m_2 \)[/tex] is the mass of the second car, [tex]\( 4264 \, \text{kg} \)[/tex]
- [tex]\( r \)[/tex] is the distance between the cars, [tex]\( 5 \, \text{m} \)[/tex]

Plugging these values into the formula, we get:

[tex]\[ F_{\text{gravity}} = \frac{(6.67 \times 10^{-11}) \times 2565 \times 4264}{5^2} \][/tex]

First, calculate the denominator:

[tex]\[ 5^2 = 25 \][/tex]

Next, compute the numerator:

[tex]\[ (6.67 \times 10^{-11}) \times 2565 \times 4264 \][/tex]

Combining the two results:

[tex]\[ F_{\text{gravity}} = \frac{(6.67 \times 10^{-11}) \times 2565 \times 4264}{25} \][/tex]

The result of this computation is:

[tex]\[ F_{\text{gravity}} = 2.92 \times 10^{-5} \, \text{N} \][/tex]

Therefore, the gravitational force between the two cars is [tex]\( 2.92 \times 10^{-5} \)[/tex] Newtons.

The correct answer is:

B. [tex]\( 2.92 \times 10^{-5} \, \text{N} \)[/tex]