Two objects attract each other with a gravitational force of magnitude 9.5 x10^-9 N when separated by 19.4 cm

Two objects attract each other with a gravitational force of magnitude 9.5 x 10^-9 N when separated by 19.4 cm. If the total mass of the objects is 5.04 kg, what is the mass of each?

heavier mass _______kg

lighter mass _______kg

This problem can be solved using the Law of Universal Gravitation:

F = (G)(m1)(m2) / r^2

where

F = force of gravity (in N)
G = gravitational constant = 6.67X10^-11 N m^2 / kg^2
m1 = mass of the first object (in kg)
m2 = mass of the second object (in kg)
r = center-to-center distance between the masses (in m)



F = (G)(m1)(m2) / r^2

(9.5 x 10^ -9) = (6.67 x 10^-11)(m1)(m2) / (0.194 m)^2

(m1)(m2) = 5.36


Let m2 = 5.04 - m1:


5.04 m1 - (m1)^2 - 5.36 = 0

(m1)^2 - 5.04 m1 + 5.36 = 0


Using the quadratic equation, m1 = 3.52; therefore, m2 = 1.52.


The heavier mass = 3.52 kg
The lighter mass = 1.52 kg


Hope this helps...good luck!