1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Classical Mechanics(linear acceleration)
  1. Classical mechanics (Replies: 3)

  2. Classical Mechanics (Replies: 3)

  3. Classical Mechanics (Replies: 3)

Loading...