College

We appreciate your visit to A spacecraft in the shape of a long cylinder has a length of 100 m and its mass with occupants is 1 480 kg It. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1,480 kg. It has strayed too close to a black hole having a mass 90 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 field acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole?

(Note: 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.)

Answer :

Answer:

2352645198509.9604 m/s²

Explanation:

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

M = Mass of black hole = [tex]90\times 1.989\times 10^{30}\ kg[/tex]

[tex]R_{f}[/tex] = 10000+100 m

[tex]R_{sb}[/tex] = Distance between the nose and the center of the black hole = 10000 m

The difference in the gravitational field in this system is given by

[tex]\Delta F=\dfrac{GMm}{R_{f}^2}-\dfrac{GMm}{R_{sb}^2}\\\Rightarrow \Delta g=GM\left(\frac{1}{R_f^2}-\frac{1}{R_{sb}^2}\right)\\\Rightarrow g=6.67\times 10^{-11}\times 90\times 1.989\times 10^{30}\left(\frac{1}{(10000+100)^2}-\frac{1}{10000^2}\right)\\\Rightarrow \Delta g=-2352645198509.9604\ m/s^2[/tex]

The acceleration is 2352645198509.9604 m/s²

Thanks for taking the time to read A spacecraft in the shape of a long cylinder has a length of 100 m and its mass with occupants is 1 480 kg It. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

The difference in the gravitational field acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole will be - 2.35 ×10¹⁶ m/sec.

What is the gravitational field?

An imaginary field in which the gravitational force is observed is known as the gravitational field.

The given data in the problem is;

G is the gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

M is the Mass of the black hole = 90 ×1.989×10³⁰ Kg

[tex]R_f[/tex] is the final radius = 10000+100 m

R₁₂ is the distance between the nose and the center of the black hole=10000 m

The gravitational field is found by the difference in the gravitational force;

[tex]\rm \trianglr F= \frac{GmM}{R_f^2} - \frac{GMm}{R_{12}^2} \\\\ \triangle g = GM(\frac{1}{R_f} )^2-(\frac{1}{R_{12}} )^2 \\\\ \triangle g = 6.67 \times 10^{-11}\times 90 \times 1.989 \times 10^{30} (\frac{1}{10100} )^2-(\frac{1}{10000}} )^2 \\\\ \triangle g = -2.35 \times 10^{16}\ m/sec^2[/tex]

Hence the difference in the gravitational field is -2.35 ×10¹⁶ m/sec.

To learn more about the gravitational field refer to the link;

https://brainly.com/question/26690770