Question

Three 5.0 kg spheres are distributed as follows. Sphere A is located at the origin, sphere B is located at x = 0.30 m y = 0 m, and sphere C is located at x = 0 m and y = 0.40 m. Find the net gravitational force vector that sphere A experiences.

Answer 1

Given

mass of spheres

mA = = mB= mC = 5 kg

located at

mA at (0m,0m),mB at (0.3m,0m), mC at (0m,0.4m)

we know that the graviational force between two bodies of m1,m2 separated by a distanc d is

   Fg = G m1*m2/d^2; G is universla gravitaional constant = 6.674*10^-11 m3 / kg s2

so F AB = 6.674*10^-11*5*5/(0.3)^2 N = 1.8538899*10^-8 N, along x -axis

F Ac = 6.674*10^-11*5*5/(0.4)^2 N = 1.0428125*10^-8 N, along y- axis

net force is = sqrt(FAB^2+FAC^2+2*FAB*FAC*cos90)
      

   = sqrt((1.8538899*10^-8)^2+(1.0428125*10^-8)^2+2*1.8538899*10^-8*1.0428125*10^-8*cos90)
      
   = 2.1270556343167*10^-8 N

the direction is theta = arc tan ((1.0428125*10^-8)/(1.8538899*10^-8))

       theta = 29.3577 degrees