A heavier mass m1 and a lighter mass m2 are 19.0 cm apart and experience a gravitational force of attraction that is 9.20 x 10^-9 N in magnitude. The two masses have a combined value of 5.80 kg. Determine the value of each individual mass.

answers:

m2 = 1.05 kg and m1 = 4.75 kg

Explanation:

the gravitational force is given by:

Fg = Gm1*m2 / (r^2)

9.20*10^-9 = [ (6.67*10^-11) * (m1*m2) ]/[ (19*10-2) ^2]

(m1*m2) = 4.98 kg^2

m1 = 4.98/m2 kg

but we given that:

m1 + m2 = 5.80 kg

4.98/m2 + m2 = 5.80

4.98 + (m2) ^2 = 5.80*m2

(m2) ^2 - 5.80*m2 + 4.98 = 0

by solving the quadratic equation above:

m2 = 4.75 kg or m2 = 1.05 kg

due to that from the information, m2 has a lighter mass, then m2 = 1.05 kg.

then m1 = 5.80 - 1.05 = 4.75 kg.