A uniform sphere with mass 60.0 kg is held with its center at the origin, and a second uniform sphere with mass 80.0 kg is held with its center at the point ?x = 0, y = 3.00 m. (a) What are the magnitude and direction of the net gravitational force due to these objects on a third uniform sphere with mass 0.500 kg placed at the point ?x = 4.00 m, ?y = 0? (b) Where, other than infinitely far away, could the third sphere be placed such that the net gravitational force acting on it from the other two spheres is equal to zero?

Step 1 of 3 a) m1m2 F 1 G r2 13 11 2 =6.673×10 N.m /kg ×60 kg×0.500 kg = (4 m) 10 = 1.251 × 10 N m2m3 F 1 G r2 23 11 2 =6.673×10 N.m /kg ×80 kg×0.500 kg = (5 m) 10 = 1.068 × 10 N Step 2 of 3 10 F 1x = 1.251 × 10 N, F 1y= 0 10 11 F 2x = F co2 = (1.068 × 10 N)(0.8) = 8.544 × 10 N 10 11 F 2y = F si2 = (1.068 × 10 N)(0.6) = 6.408 × 10 N F x F 1x + F 2x 10 11 = 1.251 × 10 N + 8.544 × 10 N = 2.105 × 1010N F y F 1y+ F2y 11 = 0 + 6.408 × 10 N = 6.408 × 1011N 2 2 F = F x F y 10 2 11 2 = ( 2.105 × 10 N) + (6.408 × 10 N) = 2.2 × 1010N 11 N tan = Fy = 6.408×10 Fx 2.105×10N = 163 0