To determine the gravitational force between you and your textbook, we'll use Newton's Law of Gravitation, which is given by the formula:
[tex]\[ F_{\text{gravity}} = \frac{G \cdot m_1 \cdot m_2}{r^2} \][/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 your mass, [tex]\( 72 \, \text{kg} \)[/tex]
- [tex]\( m_2 \)[/tex] is the mass of the textbook, [tex]\( 3.7 \, \text{kg} \)[/tex]
- [tex]\( r \)[/tex] is the distance between you and the textbook, [tex]\( 0.33 \, \text{m} \)[/tex]
Now we'll plug these values into the formula step-by-step.
1. Calculate the product of the masses:
[tex]\[ m_1 \times m_2 = 72 \, \text{kg} \times 3.7 \, \text{kg} = 266.4 \, \text{kg}^2 \][/tex]
2. Calculate the square of the distance:
[tex]\[ r^2 = (0.33 \, \text{m})^2 = 0.1089 \, \text{m}^2 \][/tex]
3. Plug into the formula:
[tex]\[ F_{\text{gravity}} = \frac{6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \times 266.4 \, \text{kg}^2}{0.1089 \, \text{m}^2} \][/tex]
4. Multiply the constant G by the product of the masses:
[tex]\[ 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \times 266.4 \, \text{kg}^2 = 1.776408 \times 10^{-8} \, \text{N} \cdot \text{m}^2 \][/tex]
5. Divide by the square of the distance:
[tex]\[ \frac{1.776408 \times 10^{-8} \, \text{N} \cdot \text{m}^2}{0.1089 \, \text{m}^2} \approx 1.631669 \times 10^{-7} \, \text{N} \][/tex]
Therefore, the gravitational force between you and your textbook is approximately:
[tex]\[ 1.63 \times 10^{-7} \, \text{N} \][/tex]
So the correct answer is:
[tex]\[ \text{B. } 1.63 \times 10^{-7} \, \text{N} \][/tex]
