13- A spacecraft in the shape of a long cylinder has a length of 100 m, and its
ID: 2253536 • Letter: 1
Question
13-A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 620 kg. It has strayed too close to a black hole having a mass 107 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.
13-A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 620 kg. It has strayed too close to a black hole having a mass 107 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.Explanation / Answer
a)the total force on the spacecraft is
F = (GMm/r^2)
where G = 6.67 x 10^-11 Nm^2/kg^2,M = 107 x 2 x 10^30 kg,m = 1620 kg and r = 10.1 km = 10.1 x 10^3 m
b)the difference in gravitational fields is
dg = (GM/r1^2) - (GM/r2^2)
where r1 = 10.0 km = 10.0 x 10^3 m and r2 = 10.1 km = 10.1 x 10^3 m
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