Question

# A 190-kg object and a 490-kg object are separated by 4.40 m. (a) Find the magnitude...

A 190-kg object and a 490-kg object are separated by 4.40 m.

(a) Find the magnitude of the net gravitational force exerted by these objects on a 63.0-kg object placed midway between them.
(N)

(b) At what position (other than an infinitely remote one) can the 63.0-kg object be placed so as to experience a net force of zero from the other two objects?
(m from the 490 kg mass toward the 190 kg mass)

Force = G * M1 * M2 /r^2

When the 63 kg particle feels the same force of attration to the 190 and 490 kg objects, the 63 kg object is in equlibrium, so net force = 0 N

G * 490 * 63 /r1^2 = G * 190 * 63/r2^2

490/r1^2 = 190/r2^2

490 * r2^2 = 190 * r1^2

r2^2/ r1^2 = 190/490 = 13/28

r2/r1 = (19/49)^0.5

r2 = r1 * (19/49)^0.5

The is ratio of distances.

The distance to the 490 object is (19/49)^0.5 * the distance to the 190 kg object

If the 190-kg object and a 490-kg object are separated by 4.40 m, r1 + r2 = 4.40

Now you have 2 equations in 2 variables, solve for r1and r2

r1 + r2 = 4.40

r2 = r1 * (19/49)^0.55

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