Question

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' = _

Answer 1

`F'=-2G(m_1m_2)/(d^3)`

Step-by-step explanation:

Given that

Force between two masses

`F=G(m_1m_2)/(d^2)`

Where G is the constant

`m_1,m_2` is the masses

d is the distance between masses.

To find the rate of change of force with distance d

`F=gm_1m_2d^(-2)`

`(DF)/(Dd)=-2Gm_1m_2d^(-3)`

`F'=(DF)/(Dd)`

`F'=-2G(m_1m_2)/(d^3)`