A 195-kg object and a 495-kg object are separated by 4.80 m. In order to experience zero net force, the third object of 49 kg should be placed 1.85 m from the 195-kg object.
The formula for the gravitational force between 2 objects is given by:
F = G ⋅ M ⋅ m/r²
Where:
G = gravitational constant = 6.674×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²
M = mass of object 1
m = mass of object 2
r = distance between 2 objects
In the given problem, let:
M1 = 195 kg
M2 = 495 kg
m = 49 kg
a) m is placed in the middle of M1 and M2
r = 4.8/2 = 2.4
Force on m exerted by M1
F1 = G ⋅ 195 ⋅ 49/(2.4)² = 1.1×10⁻⁷ N
Force on m exerted by M2
F2 = G ⋅ 495 ⋅ 49/(2.4)² = 2.8×10⁻⁷ N
Net force = (2.8 - 1.1) ×10⁻⁷ = 1.7 ×10⁻⁷ N
b) Net force on m = 0
Let d be the distance between M1 and m, then the distance between M2 and m is (4.8 - d)
r = 4.8/2 = 2.4
F1 = F2
G ⋅ 195 ⋅ 49/(d)² = G ⋅ 495 ⋅ 49/(4.8 - d)²
4.8 - d = 1.59 d
2.59 d = 4.8
d = 1.85 m
Hence, the object m should be placed 1.85 m from M1 so that the net force on it = 0
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