011 (part 1 of 2) 10.0 points Given: G= 6.67259×10-11 Nm2/kg2 A spacecraft in th

Question

011 (part 1 of 2) 10.0 points Given: G= 6.67259×10-11 Nm2/kg2 A spacecraft in the shape of a long cylinder has a a mass with occupants of 1530 kg. It has strayed in too close to a 1 km radius black hole having a mass 94.1 times that of the Sun (see the figure) If the nose of the spacecraft points toward the center of the black hole, and if the distance between the nose of the spaceship and the black hole's center is 10.4 km, determine the gravitational acceleration of the spaceship due to the black hole. Answer in units of m/s2. 012 (part 2 of 2) 10.0 points What is the difference in the acceleration felt by the occupants in the nose of the 90.7 m ship (those nearest the black hole) and those in the rear of the ship (those farthest from the black hole)? Answer in units of m/s2.

Explanation / Answer

011. a = G M / r^2

a = (6.67 x 10^-11) (94.1 x 1.99 x 10^30) / (10.4 x 10^3 )^2

a = 1.155 x 10^14 m/s^2 ........Ans

012: a1 = G M / r^2 and a2 = G M / (r + L)^2

a1 - a2 = G M [ 1 / r^2 - 1/(r + L)^2]

= (G M / r^2(r+L)^2) [ 2 r L + L^2]

r + L = r

and 2 r L + L^2 = 2 r L

a1 - a2 = G M (2 r L) / (r^4)

= (6.67 x 10^-11)(94.1 x 1.99 x 10^30) (2 x 10.4 x 10^3 x 90.7) / (10.4 x 10^3)^4

= 2.01 x 10^12 m /s^2

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