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Homework Help: Steel Sphere

  1. Aug 6, 2005 #1
    A steel sphere sits on top of an aluminum ring. The steel sphere (a (average
    coefficient of linear expansion) = 1.1*10^-5/C) has a diameter of 4 cm at 0
    C. The aluminum ring (a = 2.4*10^-5/C) has an inside diameter of 3.9940 cm at 0 C. Closest to which temperature given will the sphere just fall through the ring?

    I thought that if I took the a*L*deltaT(aluminum ring) - a*L*deltaT(steel) =
    1*10^-4 (negative difference of diameters, sphere - ring), I would get the
    right answer. However, I wasn't all that close (ended up being 208 C, and I
    got an answer much less than that). I was wondering if there was a better way to approach this problem? Thanks a lot
     
  2. jcsd
  3. Aug 6, 2005 #2

    Doc Al

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    Staff: Mentor

    You know the diameters of the aluminum and steel at T = 0. Figure out the diameter of each as a function of [itex]\Delta T[/itex]. Then solve for the temperature at which the diameters are equal.
     
  4. Aug 6, 2005 #3
    This has definitely helped me, but I'm stumped on what to do about the deltaL in thermal expansion equation. And if I do figure that out, what do I do to figure out T?

    Would it be deltaL/L*a(steel) + deltaL/L*a(aluminum) = T?

    Thank you a ton
     
  5. Aug 7, 2005 #4

    Doc Al

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    Staff: Mentor

    The diameter at temperature T equals the original diameter (at 0 degrees) plus the change in diameter from the temperature increase ([itex]\Delta T = T[/itex]):
    [tex]D = D_0 + D_0 \alpha T[/tex]

    Use this to solve for the temperature at which both diameters are equal.
     
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