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Задача Задача №2660949
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Аноним
22 января 2025 06:33 · публичный вопрос
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Аноним

m2=2m= m2=8m= r=4M G=6,67•10-11 в кв HM 2 в кв/кг2 в кв F-?

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22 января 2025 06:33

To calculate the gravitational force \( F \) between two masses using Newton's law of universal gravitation, the formula is:

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

Where:

  • \( F \) is the gravitational force
  • \( G \) is the gravitational constant (\( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))
  • \( m_1 \) and \( m_2 \) are the masses
  • \( r \) is the distance between the centers of the two masses

From your input:

  1. You have \( m_1 = 2m \) and \( m_2 = 8m \).
  2. The distance \( r = 4 \, \text{m} \).

Now, substituting in the values:

\[ m_1 = 2m, \quad m_2 = 8m \] \[ r = 4 \, \text{m} \] \[ G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \]

Now substitute into the formula for \( F \):

\[ F = \frac{(6.67 \times 10^{-11}) \cdot (2m) \cdot (8m)}{(4)^2} \]

Calculating \( r^2 \):

\[ r^2 = 4^2 = 16 \]

Now substitute \( r^2 \) into the expression for \( F \):

\[ F = \frac{(6.67 \times 10^{-11}) \cdot (16m^2)}{16} \]

Now simplify:

\[ F = 6.67 \times 10^{-11} \cdot 2m^2 = 1.334 \times 10^{-10} m^2 \text{ N} \]

So, the gravitational force \( F \) between the two masses is:

\[ F = 1.334 \times 10^{-10} m^2 \text{ N} \]

This result depends on the mass \( m \) which was not specified in the original prompt. If you have the value of \( m \), you can substitute it to find the exact force.