Question

A heavier mass m₁ and a lighter mass m₂ are 18.5 cm apart and experience a gravitational force of attraction that is 8.80 x 10⁻⁹ N in magnitude. The two masses have a combined value of 5.40 kg. Determine the value of each individual mass.

m₁ = ____ kg
m₂ = ____ kg

Answer 1

m₁ is 4.37 kg and m₂ is 1.03 kg

Step-by-step explanation:

Sum of masses = m₁ + m₂ = 5.40 kg

m₂ = 5.4 - m₁

We have gravitational force

`F=(Gm_1m_2)/(r^2)`

G = 6.674 x 10⁻¹¹ Nm²/kg²

r = 18.5 cm = 0.185 m

F = 8.80 x 10⁻⁹ N

Substituting,

`8.8* 10^(-9)=(6.674* 10^(-11)m_1m_2)/(0.185^2)\\\\m_1m_2=4.513`

m₁ x (5.4-m₁) = 4.513

5.4m₁ - m₁² = 4.513

m₁² - 5.4m₁ + 4.513 = 0

m₁ = 4.37kg or m₁ = 1.03 kg

If m₁ = 4.37 kg we have

m₂ = 1.03 kg

If m₁ = 1.03 kg we have

m₂ = 4.37 kg

So Let us consider

m₁ = 4.37 kg and m₂ = 1.03 kg