The magnitude of the gravitational force becomes 240 N
Explanation:
The magnitude of the gravitational force between two objects is given by:
[tex]F=G\frac{m_1 m_2}{r^2}[/tex]
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant
m1, m2 are the masses of the two objects
r is the separation between them
We notice that the gravitational force is inversely proportional to the square of the distance, [tex]F\propto \frac{1}{r^2}[/tex]. Since G, m1 (the mass of the black hole) and m2 (of the spaceship) in our problem are constant, we can rewrite the equation as
[tex]F=\frac{k}{r^2}[/tex]
Which can be rewritten as
[tex]Fr^2=k[/tex] (1)
At the beginning, when the distance is
[tex]r_1=10^{14} m[/tex]
The force is
[tex]F_1=60 N[/tex]
and later the distance is halved, so
[tex]r_2 = \frac{r_1}{2}[/tex]
We can rewrite eq. (1) as
[tex]F_1 r_1^2 = F_2 r_2^2[/tex]
where F2 is the magnitude of the force when the distance is halved. Substituting,
[tex]F_2 = \frac{F_1 r_1^2}{r_2^2}=\frac{F_1 r_1^2}{(r_1/2)^2}=4F_1 = 4(60 N)=240 N[/tex]
Learn more about gravitational force:
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