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Nov
19
comment Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?
You're right - thanks. I've corrected this in the original question now.
Nov
19
awarded  Editor
Nov
19
revised Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?
Correct algebra error pointed out by Peter Shor.
Nov
17
awarded  Teacher
Nov
17
answered Why is the nucleus of an Iron atom so stable?
Nov
17
awarded  Scholar
Nov
17
accepted Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?
Nov
17
comment Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?
[cont] My previous approach using integrals assumed R << L, hence r << z, so your expression for V(z) simplifies to mG int{ (1/(z-z'))dz} (where m = M/L = 2pi.R.rho = mass/unit length). This fails though because you end up with V(0) = [-ln(z')]{0,L/2} = ln(L/2) + infinity. Still not entirely sure why this doesn't work - I suspect because r << z is not true when z -> 0.
Nov
17
comment Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?
That's a great answer, thanks. I'm still surprised to see R in the final answer but glad to see it matches what you'd intuitively expect - ie for R << L small changes in R make little difference to the final answer (ln(x) is fairly flat for large x).
Nov
17
awarded  Supporter
Nov
16
comment Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?
@Kenny - you're right that the gravity field at the end of the rod is infinite, for nonzero linear density. And clearly in the real world atoms are separate in space, so the 'infinite' problem doesn't arise. But the question remains how to approximate the force/pressure in the middle of this bar. To avoid the infinite problem (linear density) I've instead broken my bar into discrete pieces - but as the number of pieces increases (Ndiv = 2, 4, 6 -> large), the answer keeps increasing which doesn't make sense.
Nov
16
awarded  Commentator
Nov
16
comment Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?
@Mark - yes, but I'm a little rusty. Eg with Kenny's explanation, I don't see where the original integral comes from, but I can follow the rest (I wouldn't be able to solve the integral myself but can happily accept how to go from one stage to the next).
Nov
16
comment Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?
Thanks. Clearly the pressure does tend to infinity as the area on which it acts tends to zero. But what I have in mind is a "long, thin" bar - ie where the thickness of the bar is small compared to the length. What happens to your formula if you ignore the bar thickness (assume e << L), and try to calculate instead (stress * area) at the centre?
Nov
16
comment Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?
Clarification: as TheMachineCharmer correctly points out, the net force in the middle of the bar is zero. But what I'm trying to find is the pressure exerted on you at the middle of the bar, due to the weight of both halves of the bar. Or to ask another way, if you cut the bar in half and put a spring between the two halves, how much would the spring contract?
Nov
16
awarded  Student
Nov
16
asked Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?