Considering the Law of Universal Gravitation, the mass of the second object is 78090.19 kg.
The Law of Universal Gravitation is a law that states that bodies, by the simple fact of having mass, experience a force of attraction towards other bodies with mass, called gravitational force.
This law establishes that every particle attracts any other particle with a force directly proportional to the product of the masses of both and inversely proportional to the square of the distance that separates them:
[tex]F=G\frac{m1m2}{r^{2} }[/tex]
where m1 and m2 are their masses; r the distance between them and G a universal constant that is called the constant of gravitation.
In this case, you know:
- F= 0.128 N
- G=6.67× 10⁻¹¹ Nm²/kg²
- m1= 1300 kg
- m2= ?
- r= 0.23 m
Replacing:
[tex]0.128 N=6.67x10^{-11}\frac{Nm^{2} }{kg^{2} } \frac{1300 kg m2}{(0.23 m)^{2} }[/tex]
Solving:
[tex]0.128 N=1.639x10^{-6}\frac{N}{kg }x m2[/tex]
m2=0.128 N ÷ 1.639×10⁻⁶ [tex]\frac{N}{kg}[/tex]
m2=78090.19 kg
In summary, the mass of the second object is 78090.19 kg.
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