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Mechanics Pulley question !

  1. Aug 12, 2012 #1
    1. The problem statement, all variables and given/known data

    A mass 4m lying on a rough horizontal table is connected by a string,
    passing over a pulley, to another mass 3 m hanging freely. The pulley (regarded
    as a disk) has mass 4 m and rotates freely about a polar axis parallel to the
    edge of the table. The coefficient of kinetic friction between the mass and the
    table is μ=3/8. Assuming that the string does not slip on the pulley, Find the
    common acceleration of the masses and show that the ratio of the tensions in
    the string on either side of the pulley is T1 : T2 = 13 : 15. (You may assume
    that the moment of inertia of a disk of radius r and mass m about a polar axis
    through the disk is I =1/2 M r^2)

    [D] Attempt
    acceleration

    4mg-t=4a
    t-3mg=3A

    1g=7a
    10=7a
    a=10/7
    a=1.428



    Tension 2:
    4m(g)=4m(10)=40m

    3/8=T2/40 , 120/8 = T2 , T2=15m

    Tension 1:
    3(10)=30



    am i on the right track?



    Thanks for the help have a big exam and this is a common question , having problems with it because the pulley is moving and dont know how it effects the acceleration .solution would be fantastic !!:shy:
     
    Last edited: Aug 12, 2012
  2. jcsd
  3. Aug 12, 2012 #2
    The force of gravity on the hanging mass will not only accelerate the system of masses, but also cause the pulley to rotate.
     
  4. Aug 12, 2012 #3
    Thanks for your help ! so the pulley does not effect the common acceleration? does the pulley due to its mass have any bearing on the tension of the hanging mass?
     
  5. Aug 12, 2012 #4
    It does effect the acceleration of the mass system because as the mass drops, energy is transferred into the pulley as well, instead of remaining in the system.
     
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