Answer to Question #173294 in Physics for christian espiritu

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