Volume of nebula needed to form a star with same number of atoms as sun

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To determine the volume of a nebula needed to form a star with the same number of atoms as the sun, the mean separation of atoms in the nebula is 2.3x10^-3 m, while the sun has a radius of 7.0x10^8 m and a mean distance between atoms of 1.0x10^-10 m. The volume of the sun is calculated to be 1.4x10^27 m^3. A user initially calculated the required nebula volume as 3.22x10^34 m^3, but the book states it should be 1.8x10^49 m^3. The discussion highlights frustrations with the lack of detailed solutions in physics textbooks and the importance of clear working in problem-solving.
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1. Question: In one region of a nebula the mean separation of atoms is 2.3x10^-3 m. What volume of the nebula contains enough atoms to make a star, similar to the sun, of radius 7.0x10^8 m within which the mean distance between atoms is 1.0x10^-10m?



2. Volume of sphere 4/3(pi(r^3 ))


3. Volume sun = 1.4x10^27 m^3. I thought that atoms in sun would be volume divided by separation distance and therefore volume of nebula that contains same number of atoms is atoms times separation distance (of nebula)? my answer was 3.22x10^34 m^3 answer in book is 1.8x10^49 m^3

I really hate these OCR A2 physics books because they don't work through any of the questions..
Help please!
 
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I agree i had the exact same question and objection to the books, i arrived at the same conclusion as you, did you ever resolve the question?
 
I'm sorry that was a while ago now and I can't remember ...
 
HAha fine, I'l go over it with my tutor tomorrow. Well done for putting your working so clearly, it helped.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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