A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass

Question

A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 2 000 kg. It has strayed too close to a black hole having a mass 101 times that of the Sun. The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km.

A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 2 000 kg. It has strayed too close to a black hole having a mass 101 times that of the Sun. The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km. What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in acceleration grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.)

Explanation / Answer

According to Newton's Laws of Gravitation, the force is determined by the mass and by the radius. The radius is between the centres of two objects. So for part (a) the radius will be 10 000m + 50m= 10050m.
Mass of the black hole= 1.791E32 kg

So the force will be
Fg=Gmm/r^2
=(6.67E-11)(1.791E32)(2000)/(10050^2)
=2.365E17 N

The difference in the force fields will be
delta g=Gm/(r1)^2-Gm/(r2)^2
=(6.67E-11)(1.791E32)/(10000)^2 - (6.67E-11)(1.791E32)/(10100)^2
=1.194597E14 - 1.1710587E14
=2.3538 N/kg

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