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Newton's Law of Universal Gravitation states that the force F between two masses, m1 and m2, is given below, where G is a constant and d is the distance between the masses. Find an equation that gives an instantaneous rate of change of F with respect to d. (Assume m1 and m2 represent moving points.)F = (Gm1m2) / d2F' = _

Respuesta :

Answer:

[tex]F'=-2G\dfrac{m_1m_2}{d^3}[/tex]

Explanation:

Given that

Force between two masses

[tex]F=G\dfrac{m_1m_2}{d^2}[/tex]

Where G is the constant

[tex]m_1,m_2[/tex] is the masses

d is the distance between masses.

To find the rate of change of force with distance d

[tex]F=gm_1m_2d^{-2}[/tex]

[tex]\dfrac{DF}{Dd}=-2Gm_1m_2d^{-3}[/tex]

[tex]F'=\dfrac{DF}{Dd}[/tex]

[tex]F'=-2G\dfrac{m_1m_2}{d^3}[/tex]

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