a) The magnitude of the net gravitational force exerted by these objects on a 53.0 kg is 6.03 * 10¹¹ N
b) By placing object of 53.0 kg 1.976 m from 175 kg object and 1.324 m from 475 kg object.
Mass of an object-1= M₁ = 175 kg
Mass of an object-2= M₂ = 475 Kg
Distance between M₁ & M₂ = 3.90 m
Mass of an object-3 = M₃ = 53 Kg
If M₃ placed midway between them M₁ & M₂.
Force on M₃ due to M₁
Distance between M₁ & M₃, r = 3.90/2 = 1.95
F = G(M₁*M₃/r²)
F = 6.67 x 10¹¹(175*53/ 1.95²)
F = 16,269.33*10¹¹ = 1.62 * 10⁷ N
Force on M₃ due to M₂
Distance between M₂ & M₃, r' = 3.90/2 = 1.95
F' = G(M₂*M₃/r²)
F = 6.67 * 10₁₁ ( 475 * 53/ 3.8)
F = 44188.75 * 10¹¹ = 4.41 * 10⁷ N
Net force on M₃:
F' + F = 4.41 * 10⁷ N + 1.62 * 10⁷ N = 6.03 * 10¹¹ N
The magnitude of the net gravitational force exerted by these objects on a 59.0 kg is 6.03 * 10¹¹ N.
b) Distance between M₁ & M₂ = r = 3.90 m
Let the distanced between M₁ & M₃ be r
Force experienced by M₃ due to M₁ :
f = G(M₁*M₃/r²)
Let the distanced between M₂ & M₃ be r'
Force experienced by M₃ due to M₂:
f' = G(M₂*M₃/r²)
Net force equal to zero, then :
f = f'
G(M₁*M₃/r²) = G(M₂*M₃/r'²)
6.18*10⁷/r₂² = 16.7*10₇/r'²
r = 1.4914 * r'
R = r+r'
3.90 m = 1.4914\times r' + r'
r' = 1.324 m
r = 1.976 m
Therefore, the magnitude of the force on M₃ is 6.03 * 10¹¹ N and by placing object of 53.0 kg 1.976 m from 175 kg object and 1.324 m from 475 kg object.
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