- #1
alphaj
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Homework Statement
Muscle can be torn apart by a force of 100,000 N applied across an area of 1 m2. A 10 cm2 muscle therefore will be torn by a force of 100 N.
If a student of average size were being lowered into a black hole of 1 solar mass, at about what distance from the hole's center will he be torn apart?
2. (What I thought was a) Relevant equation
RSchwarzschild= (2MG)/c2
Where M is the mass of the black hole; G is the gravity constant; c is the speed of light.
(seen here: http://hyperphysics.phy-astr.gsu.edu/hbase/astro/blkhol.html#c2)
The Attempt at a Solution
I did some background research on black holes and I thought that if I calculated the Schwarzschild radius, I would be able to identify the event horizon (defined as the last distance at which light can escape the pull of a black hole) of the black hole, and thus, that would tell me the distance from which the student would be torn apart.
RSchwarzschild= (2MG)/c2
= [2(1 solar mass)(6.67 x 10-11 Nm2/kg2]/(2.998 x 108 m/s)2
R = 1.48x10-27 m
I think this would be the correct answer, but it doesn't use any of the numerical givens other than the mass of the black hole.
When I consider the givens regarding surface area and force; I can tell that I am supposed to use an estimate of an 'average student's size' to attain my answer. If I estimate that the average person is about 1.75 m2 (estimate using numbers from BSA https://en.wikipedia.org/wiki/Body_surface_area), then I believe I can say that 100000 N is to 1 m2, as x N is to 1.75 m2 and cross multiply to find that it would take x=175000 N of force to tear apart the student's muscles. But, I am unsure of how to relate this force to black holes and distance.
Any help or hints would be appreciated! Thank you.