Objects with masses of 250 kg and a 550 kg are separated by 0.340 m. (a) Find th

Question

Objects with masses of 250 kg and a 550 kg are separated by 0.340 m.
(a) Find the net gravitational force exerted by these objects on a 41.0 kg object placed midway between them.
magnitude


Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N
direction


(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 550 kg mass

Explanation / Answer

Force = G * M1 * M2 /r^2 When the 41 kg particle feels the same force of attration to the 250 and 550 kg objects, the 34 kg object is in equlibrium, so net force = 0 N G * 550 * 41 /r1^2 = G * 250 * 41/r2^2 550/r1^2 = 250/r2^2 550 * r2^2 = 250 * r1^2 r2^2/ r1^2 = 250/550 = 5/11 r2/r1 = (5/11)^0.5 r2 = r1 * (5/11)^0.5 The is ratio of distances. The distance to the 550 object is (5/11)^0.5 * the distance to the 250 kg object If the 250-kg object and a 560-kg object are separated by 4.10 m, r1 + r2 = 4.10 Now you have 2 equations in 2 variables, solve for r1and r2 r1 + r2 = 4.10 r2 = r1 * (5/11)^0.55

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