m1=200кг m2=300кг f=5*10^-15 н r-?
To find the distance \( r \) between the two masses \( m_1 = 200 \, \text{kg} \) and \( m_2 = 300 \, \text{kg} \) given the gravitational force \( F = 5 \times 10^{-15} \, \text{N} \), we can use Newton's law of universal gravitation:
\[ F = G \frac{m_1 m_2}{r^2} \]
where \( G \) is the gravitational constant, approximately \( 6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \).
Rearranging the formula to solve for \( r \):
\[ r^2 = G \frac{m_1 m_2}{F} \]
\[ r = \sqrt{G \frac{m_1 m_2}{F}} \]
Plugging in the values:
\[ r = \sqrt{(6.674 \times 10^{-11}) \frac{(200)(300)}{5 \times 10^{-15}}} \]
Now let's calculate it step by step.
- Calculate \( m_1 m_2 = 200 \times 300 = 60000 \, \text{kg}^2 \).
- Calculate the fraction:
\[ \frac{60000}{5 \times 10^{-15}} = 1.2 \times 10^{19} \]
- Multiply this by \( G \):
\[ G \cdot 1.2 \times 10^{19} = (6.674 \times 10^{-11}) \times (1.2 \times 10^{19}) \approx 8.0088 \, \text{m}^2 \]
- Finally, take the square root:
\[ r \approx \sqrt{8.0088} \approx 2.83 \, \text{m} \]
So, the distance \( r \) is approximately \( 2.83 \, \text{m} \).
