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Block and Pulley

  1. Mar 30, 2012 #1
    1. The problem statement, all variables and given/known data

    A block of mass m=2.4kg is attached to a string that is wrapped around the circumference of a wheel of radius r=7.6cm. The wheel rotates freely about it's axis and the string wraps around it's circumfrence without slipping. Initially, the wheel rotates with an angular speed ω, causing the block to rise with a linear speed v=.29m/s.
    Find the moment of inertia of the wheel if the block rises to a height of h=7.7cm before momentarily coming to rest.

    2. Relevant equations

    Ei=Ef

    3. The attempt at a solution

    Ei=1/2mv^2+1/2Iw^2+mgy
    Ei=1/2mv^2+1/2Iw^2+0
    Ef=1/2mv^2+1/2Iw^2+mgy
    Ef=0+0+mgh
    mgh=1/2mv^2+1/2Iw^2
     
  2. jcsd
  3. Mar 30, 2012 #2
    I had found the equation
    h=(v^2/2g)(1+I/mR^2)
    and i got I=.2349
    I had to use two significant digits in my answer and I used .23 but it is saying that I need to check the rounding or number of significant digits.
     
  4. Mar 30, 2012 #3

    gneill

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    Staff: Mentor

    What value did you use for g? You should use values for constants that have more digits of accuracy than the result requires.
     
  5. Mar 30, 2012 #4
    I used 9.8 would 9.81 be better? or should I go further than that?
     
  6. Mar 30, 2012 #5
    got it! thanks!
     
  7. Mar 30, 2012 #6

    gneill

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    Staff: Mentor

    g = 9.807 m/s2 is usually good enough. I usually use g = 9.80665 m/s2 in my calculations so I never have to worry about it :smile:

    Round results, not intermediate values, so you don't lose accuracy through the calculation process.
     
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