Answer to Question #173296 in Physics for christian espiritu

Question

Four masses are located in the corners of a square. Calculate the magnitude and direction of the gravitational field at the center of the square. Given: m₁ = 85 kg, m₂ = 3 kg, m₃ = 3 kg, m₄ = 85 kg r = 8 m, G = 6.674×10–11 N·m²/kg². 

Answer 1

$E=F/m=G\frac{M}{a^2}$

$a^2+a^2=8^2\to2a^2=64\to a=4\sqrt2$

$E_1=E_4=G\frac{m_1}{a^2}=6.674\cdot10^{-11}\cdot\frac{85}{(4\sqrt2)^2}=17.7\cdot10^{-11} \ (N/kg)$

$E_2=E_3=G\frac{m_2}{a^2}=6.674\cdot10^{-11}\cdot\frac{3}{(4\sqrt2)^2}=0.6\cdot10^{-11} \ (N/kg)$

$|\vec E_1+\vec E_4|=2\cdot17.7\cdot10^{-11}\cdot\cos45°=25\cdot10^{-11}\ (N/kg)$

$|\vec E_2+\vec E_3|=2\cdot0.6\cdot10^{-11}\cdot\cos45°=0.85\cdot10^{-11}\ (N/kg)$

$E_{total}=25\cdot10^{-11}-0.85\cdot10^{-11}=24.15\cdot10^{-11}\ (N/kg)$ . Answer