Concept explainers
(a)
The proof for the statement that when
(a)
Answer to Problem 69PQ
It is showed that when
Explanation of Solution
Write the equation for the gravitational field for a mass.
Here,
Write the expression for the difference in gravitational field at a distance
Use equation (I) to find the expression for
Use equation (I) to find the expression for
Put the above two equations in equation (II).
Expand the numerator of the above equation.
It is given that
Conclusion:
Neglect
Thus, it is showed that when
(b)
The difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole.
(b)
Answer to Problem 69PQ
The difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole is
Explanation of Solution
The expression for the difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole is derived in part (a).
Write the expression for the difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole.
Conclusion:
Given that the mass of the black hole is one solar mass, the length of the person is
Substitute
Therefore, the difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole is
(c)
Whether the difference in gravitational field found in part (b) large enough to spaghettify the person.
(c)
Answer to Problem 69PQ
The difference in gravitational field found in part (b) is large enough to spaghettify the person.
Explanation of Solution
Spaghettification is the term used by Stephen Hawking to describe what happens to someone who falls feet first into a small but highly massive object. Since the gravitational field at the person’s feet is sufficiently higher than the gravitational field at the head, the person gets stretched out like a spaghetti noodle.
In part (b), it is found that the difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole is
Conclusion:
Since the feet of the person are accelerating toward the black hole
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Chapter 7 Solutions
Physics for Scientist and Engineers (Foundations And Connection; Volume I and II) LLF edition
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