A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 860 kg. It has strayed too close toa black hole having a mass 98 times that of the Sun. The nose of the spacecraft points toward the black hole, and the distancebetween the nose and the center of the black hole is 10.0 km.100 m-10.0 kmBlack hole(a) Determine the total force on the spacecraft.The total force is determined by the distance from the black hole to the center of gravity of the ship which will be close to themidpoint. N(b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear ofthe ship, farthest from the black hole? (This difference in acceleration grows rapidly as the ship approaches the black hole. Itputs the body of the ship under extreme tension and eventually tears it apart.)N/kg2.56e+12

Answered: Image /qna-images/answer/9aa6842b-1f7d-4d84-8923-ed9adcb99c96.jpg

Answered: A spacecraft in the shape of a long…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 13PQ: A massive black hole is believed to exist at the center of our galaxy (and most other spiral...

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Two black holes (the remains of exploded stars), separated by a distance of 10.0 AU (1 AU = 1.50 1011 m), attract one another with a gravitational force of 8.90 1025 N. The combined mass of the two black holes is 4.00 1030 kg. What is the mass of each black hole?
A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 000 kg. Ii has strayed too close to a black hole having a mass 100 times that of the Sun (Fig. P11.11). 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 in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in accelerations grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.)
(a) What is the approximate force of gravity on a 70kg person due to the Andromeda galaxy, assuming its total mass is 1013 than of our Sun and acts like a single mass 2 Mly away? (b) What is the ratio of this force to the person's weight? Note that Andromeda is the closest large galaxy.
A neutron star is a cold, collapsed star with nuclear density. A particular neutron star has a mass twice that of our Sun with a radius of 12.0 km. (a) What would be the weight of a 100-kg astronaut on standing on its surface? (b) What does this tell us about landing on a neutron star?
Astronomical observatrions of our Milky Way galaxy indicate that it has a mass of about 8.01011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0104 light-years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way.
Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital Speed using the following information: The mass of the galaxy is equivalent to a single mass times that at the Sun (or located 30,000 ly away.
What is the Schwarzschild radius for the black hole at the center of our galaxy if it has the mass of 4 million solar masses?
(a) Show that tidal force on a small object of mass m, defined as the difference in the gravitational force that would be exerted on m at a distance at the near and the far side of the object, due to the gravitational at a distance R from M, is given by Ftidal=2GMmR3r where r is the distance between the near and far side and rR .(b) Assume you are fallijng feet first into the black hole at the center of our galaxy. It has mass of 4 million solar masses. What would be the difference between the force at your head and your feet at the Schwarzschild radius (event horizon)? Assume your feet and head each have mass 5.0 kg and are 2.0 m apart. Would you survive passing through the event horizon?
Compute directly the gravitational force on a unit mass at a point exterior to a homogeneous sphere of matter.
A stellar black hole may form when a massive star dies. The star collapses down to a single point. Our Sun will not become a black hole because it does not have enough mass, so let us imagine a black hole with eight times the mass of the Sun. A single point has no radius, but a black hole has an effective radius known as the Schwarzschild radius. If an object gets inside the Schwarzschild radius, it never escapes. The Schwarzschild radius of an eight-solar-mass black hole is about 24 km. a. Find the escape speed using the Schwarzschild radius. b. Compare your answer to the speed of light and speculate on how these objects got the name black hole.
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.1011 solar masses. A star orbiting on the galaxy's periphery is about 6.0104 light years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.
Neutron stars are extremely dense objects formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 10.0 km. Determine the greatest possible angular speed it can have so that the matter at the surface of the star on its equator is just held in orbit by the gravitational force.

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