Objects with masses of 245 kg and a 545 kg are separated by 0.390 m. (a) Find th

Question

Objects with masses of 245 kg and a 545 kg are separated by 0.390 m.

(a) Find the net gravitational force exerted by these objects on a 41.0-kg object placed midway between them.

(b) At what position (other than infinitely remote ones) can the 41.0-kg object be placed so as to experience a net force of zero?
m from the 545-kg mass

magnitude
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. N direction ---Select--- toward the 245-kg mass toward the 545-kg mass The magnitude is zero.

Explanation / Answer

m1 = 245 kg

m2 = 545 kg

m3 = 41 kg

d = distance between m1 and m2 = 0.390 m

r = distance of m1 and m2 from m3 = 0.390/2 = 0.195 m

F13 = gravitational force on m3 by m1 = Gm1 m3 / r2 = (6.67 x 10-11) (245) (41) / (0.195)2 = 0.0000176 N

F23 = gravitational force on m3 by m2 = Gm2 m3 / r2 = (6.67 x 10-11) (545) (41) / (0.195)2 = 0.0000392 N

Net force = F23 - F13 = 0.0000392 - 0.0000176 = 0.0000216 N

since F23 is greater , net force is towards 0.0000392 N

b)

let m3 is placed at distance "a' from mass m1

Force by m1 = Force by m2

F13 = F23

Gm1 m3 / a2 = Gm2 m3 / (d - a)2

m1 / a2 = m2 / (d - a)2

245 / a2 = 545 / (0.39 - a)2

a = 0.157 m

there is no other position where 41 kg would experience net force 0 since forces do not cancel out at any other position

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