Three 9.3 kg masses are at the corners of an equilatral triangle and located in

Question

Three 9.3 kg masses are at the corners of an equilatral triangle and located in space far from any other masses.

a) if the sides of the triangle are 14.2 m long, find the magnitude of the net force F1 exerted on each of the three masses. Give your answer with four significant figures.

b) if the distance between masses is increased by a factor of 16 how will the new force compare to the initial net force? Express your answer as the ratio F2/F1 . Simplify your answer as far as possible. Thank you . PLease Explain the steps.

Explanation / Answer

a) force between two masses.

F = G M M / d^2 = (6.67 x 10^-11 x 9.3 x 9.3) / (14.2^2) = 2.86 x 10^-11 N

on each, there will be two force vectors of same magnitude and angle between them will be 60 deg.

so Fnet = sqrt[ F^2 + F^2 + 2(F)(F)cos60 ] = sqrt(3) F

Fnet = F1 = 1.732 x 2.86 x 10^-11 = 4.95 x 10^-11 N ..........Ans

b) now F' = F / 16^2 = 3.91 x 10^-3 F

and F2 = sqrt(3) x 3.91 x 10^-3 x F

hence F2/F1 = 3.91 x 10^-3

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