Physics: Aheavier 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

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Aheavier mass m₁ and a lighter mass m₂ are 18.5 cm - id1854108420, rosenthaljaneiah2010

kevinhernandez582

12.01.2022

m₁ is 4.37 kg and m₂ is 1.03 kg

Explanation:

Sum of masses = m₁ + m₂ = 5.40 kg

m₂ = 5.4 - m₁

We have gravitational force

$F=\frac{Gm_1m_2}{r^2}$

G = 6.674 x 10⁻¹¹ Nm²/kg²

r = 18.5 cm = 0.185 m

F = 8.80 x 10⁻⁹ N

Substituting,

$8.8\times 10^{-9}=\frac{6.674\times 10^{-11}m_1m_2}{0.185^2}\\\\m_1m_2=4.513$

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

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