Question

Three masses are located in the corners of an equilateral triangle. Find the magnitude and direction of the gravitational field at the center of the triangle. Given: m₁ = 22 kg, m₂ = 30 kg, m₃ = 30 kg, r = 12 cm. G = 6.674×10–11 N·m²/kg². 

Answer 1

Let $r$ is the distance between the masses and the center of an equilateral triangle. So, we have

$E_1=G\frac{m_1}{r^2}=6.674\cdot10^{-11}\cdot \frac{22}{0.12^2}\approx1.02\cdot10^{-7}\ (N/kg)$

$E_2=G\frac{m_2}{r^2}=6.674\cdot10^{-11}\cdot \frac{30}{0.12^2}\approx1.39\cdot10^{-7}\ (N/kg)$

$E_3=G\frac{m_3}{r^2}=6.674\cdot10^{-11}\cdot \frac{30}{0.12^2}\approx1.39\cdot10^{-7}\ (N/kg)$

$|\vec E_2+\vec E_3|=2\cdot1.39\cdot10^{-7}\cdot\cos60°=1.39\cdot10^{-7}\ (N/kg)$

The gravitational field at the center of the triangle

$E=1.39\cdot10^{-7}-1.02\cdot10^{-7}=0.37\cdot10^{-7}\ (N/kg)$ . Answer