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A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1000 kg. It has strayed too close to a black hole having a mass 100 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) Determine the total force on the spacecraft.

b) What is the difference in the gravitational fields acting on the occupants at the nose of the ship and those at the rear of the ship?

Answer :

The total force on the spacecraft is 1.33e17 N and the difference in gravitational fields acting on the occupants of the nose of the ship and those in the rear of the ship is 2.7e11[tex]m/s^2[/tex].

a) The total force on the spacecraft is 1.32752e17 N.

b) The difference in gravitational fields acting on the occupants of the nose of the ship and those in the rear of the ship is 2.6552e11 [tex]m/s^2[/tex].

For part a), I used the formula for the gravitational force between two objects:

F = G * (m1 * m2) /[tex]r^2[/tex]

Where:

G is the gravitational constant (6.67430e-11 N*[tex]m^2/kg^2)[/tex]

m1 is the mass of the first object (1000 kg)

m2 is the mass of the second object (M_blackhole = 100 * M_sun = 1.989e30 kg)

r is the distance between the centers of the two objects (10.0 km = 10e3 m)

Plugging in the values, I got:

F = 6.67430e-11 * (1000 kg) * (1.989e30 kg) / [tex](10e3 m)^2[/tex]

F = 1.32752e17 N

For part b), I used the formula for the gravitational field:

[tex]g = G * M / r^2[/tex]

Where:

g is the gravitational field

G is the gravitational constant[tex](6.67430e-11 N*m^2/kg^2)[/tex]

M is the mass of the object creating the gravitational field (M_blackhole = 100 * M_sun = 1.989e30 kg)

r is the distance from the center of the object creating the gravitational field (r_nose = 10e3 m - L/2 = 9.5e3 m for the nose and r_rear = 10e3 m + L/2 = 10.5e3 m for the rear)

Plugging in the values for the nose, I got

g_nose= 6.67430e-11 * (1.989e30 kg) / [tex](9.5e3 m)^2[/tex]

g_nose = 2.77587e11 [tex]m/s^2[/tex]

Plugging in the values for the rear, I got:`

g_rear = 6.67430e-11 * (1.989e30 kg) / [tex](10.5e3 m)^2[/tex]

g_rear = [tex]2.04373e11 m/s^2[/tex]

Finally, I took the difference between the two gravitational fields to find the difference:

delta_g = g_nose - g_rear

delta_g =[tex]2.77587e11 m/s^2 - 2.04373e11 m/s^2[/tex]

delta_g =[tex]7.3214e10 m/s^2[/tex]

Therefore, the total force on the spacecraft is 1.32752e17 N and the difference in gravitational fields acting on the occupants of the nose of the ship and those in the rear of the ship is 7.3214e10 [tex]m/s^2.[/tex]

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Rewritten by : Barada

Answer:

a) the total force on the spacecraft = 1.31 x 10 ∧17N

b) the difference in the gravitational fields acting on the occupants of the nose of the ship and those in the rear of the ship = 0.266 x 10 ∧13 N

Explanation:

See the attachment for step by step explanation.