Leaving the distance between the 296 kg and the 699 kg masses fixed, at what dis

Question

Leaving the distance between the 296 kg and the 699 kg masses fixed, at what distance from the 699 kg mass (other than infinitely remote ones) does the 47.6 kg mass experience a net force of zero?

Answer in units of m.

Objects with masses of 296 kg and 699 kg are separated by 0.424 m. A 47.6 kg mass is placed midway between them.

Find the magnitude of the net gravitational

force exerted by the two larger masses on the 47.6 kg mass. The value of the universal gravi- tational constant is 6.672 × 1011 N · m2/kg2.

Answer in units of N.

Explanation / Answer

(a)

The gravitational force is,

Fg = G*m1*m2 / r^2

let, net force is 0 at distance d from 699 kg

let distance b/w 296 kg and 699 kg = 1 m

G*699*47.6 / d^2 - G*296*47.6 / (1 - d)^2 = 0

699*47.6 / d^2 = 296*47.6 / (1 - d)^2

by solving this,

d = 0.605 m

(b)

net gravitational force,

Fnet = G*699*47.6 / (0.212)^2 - G*296*47.6 / (0.212)^2

put G =6.67*10^(-11)

by solving above equation,

Fnet = 2.85*10^(-5) N

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