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Homework Help: Classical Mechanics(linear acceleration)

  1. May 5, 2008 #1
    1. The problem statement, all variables and given/known data
    A reel of mass M and of radius a has tape wound round its axle
    which has radius b . The tape has negligible mass. The reel is
    initially at rest on a rough horizontal table when the free end of the
    tape is pulled horizontally by a constant force T , as shown below.
    The pull T is sufficiently small that the reel does not slide.
    Show that the resulting acceleration is given by

    a=dv/dt = a(a-b)T/M(k^2+a^2)
    where V is the velocity of the centre of the reel and k is the radius
    of gyration of the reel.

    2. Relevant equations

    not given

    3. The attempt at a solution

    working so far,

    dv/dt= r*angular acceleration(al)
    dv/dv=t*r/I i=moment of inertia

    unable to complete the proof.
    please help
  2. jcsd
  3. May 5, 2008 #2


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    Write the total kinetic energy (both rotational and translational) of the wheel as a function of v. Now the rate of change of KE is equal to T times the rate at which the tape is being reeled it. There are two things to consider for the tape rate, the wheel is rolling with velocity v and the tape is unwinding from that axis. You have to add them. BTW your given solution is clearly wrong. If a=b that formula would say the acceleration would be zero. I don't think that's right.
  4. May 5, 2008 #3


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    Hah! I'll bet I know what it is. Your figure must show the tape being pulled off of the bottom of the axle. So the v of wheel is AWAY from you. That would mean the v and unwinding are acting in opposite directions and need to be subtracted to get the net tape rate.
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