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to score. 001 (part 1 of 2) 8.0 points Objects with masses of 212 kg and 673 kg

ID: 1794825 • Letter: T

Question

to score. 001 (part 1 of 2) 8.0 points Objects with masses of 212 kg and 673 kg are separated by 0.365 m. A 61.1 kg mass is placed midway between them. 673 kg 212 kg 61.1 kg 0.365 m Find the magnitude of the net gravitational force exerted by the two larger masses on the 61.1 kg mass. The value of the universal gravi- tational constant is 6.672 × 10-11 N·m 2/kg2 Answer in units of N 002 (part 2 of 2) 10.0 points Leaving the distance between the 212 kg and the 673 kg masses fixed, at what distance from the 673 kg mass (other than infinitely remote ones) does the 61.1 kg mass experience a net force of zero? Answer in units of m.

Explanation / Answer

m1 = 212 kg

m2 = 673 kg

m3 = 61.1 kg

d = 0.365 m

a) r = d/2 = 0.1825 m

net gravitational force on central mass = (Gm3/r2)(m2 - m1)

= (6.672 x 10-11 x 61.1/(0.1825)2)(673-212) = 5.3455898 x 10-5 N

b) for net force to be zero, let r1 be required distance from 673 kg mass

Gm1m3/(d-r1)2 = Gm2m3/(r1)2

=>>> m1/(d-r1)2 = m2/(r1)2

==> 212/(0.365 -r1)2 = 673/(r1)2

=>>> ((0.365 - r1)/r1)2 = 212/673

==> (0.365 - r1)/r1 = sqrt(212/673)

==> 0.365 - r1 = 0.561255r1

=>> r1 = 0.233786247 m