Three uniform spheres of masses m1 = 3.50 kg, m2 = 4.00 kg, and m3 = 6.50 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe.

Question

Three uniform spheres of masses m1 = 3.50 kg, m2 = 4.00 kg, and m3 = 6.50 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe. The figure depicts m2 at the origin with m3 going along the x-axis to <-4.00,0>m, and m1 going along the y-axis to <0,3.00>m. The force vectors are labelled as F32 and F12.

Elena · Answer

the gravitational constant
G =6.67•10⁻¹¹ N•m²/kg²,
F₁₂ =G•m₁•m₂/y²= ...
F₃₂ =G•m₃•m₂/x²= ...
F=sqrt(F₃₂²+F₁₂²)=...
φ is the angle respectively the negative
direction of x-axis
tan φ=F₁₂/F₃₂= ...