Answer to Question #173295 in Physics for christian espiritu

Question

 Four masses are at the vertices of a square. Find the magnitude of the gravitational force on the mass m₁. Given: m₁ = 6 kg, m₂ = 80 kg, m₃ = 80 kg, m₄ = 80 kg r = 24 m. G = 6.674×10–11N·m²/kg². 

Answer 1

Let $r$ is the side of the square.

$F_2=F_4=G\frac{m_1m_2}{r^2}=6.674\cdot10^{-11}\cdot\frac{6\cdot80}{24^2}=5.56\cdot10^{-11}\ (N)$

$F_3=G\frac{m_1m_3}{(r\cdot\sqrt2)^2}=6.674\cdot10^{-11}\cdot\frac{6\cdot80}{(24\cdot\sqrt2)^2}=2.78\cdot10^{-11}\ (N)$

$F_{total}=2\cdot5.56\cdot10^{-11}\cdot\cos45°+2.78\cdot10^{-11}=10.64\cdot10^{-11}\ (N)$ . Answer