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!

Pulley with a rope

  1. Feb 4, 2017 #1
    1. The problem statement, all variables and given/known data
    a circular homogenic pulley (disk) with radius R and mass of M hanging on a axis that passes through his center,
    the pulley rotating without friction.
    we wrap the pulley with a rope with a total mass of mr and length of L and in the other side of the rope we ataching body with a mass of m* , m* is starting to go down while rotating the disk
    find the angular velocity of the pullay as function of the length of the suspanded rope -x GUF KASHIAH.jpg
    2. Relevant equations
    Ipulley=MR^2/2 - inertia torque of the pulley (in the center of mass)
    Irope=mr*R^2 - inertia torque of the rope (at the beginning when wrapped)
    E=0.5Iω^2 -energy to rotate the disk pulley
    U=m*gh-potential energy of the mass m* at the beginning (h is not given)
    3. The attempt at a solution
    iv`e tried to do equations of preserving energy between the start point when we have only potential of the mass m* and to equalize it to the point when we have a total hanging mass of m**= m* + mr(x/L) in a height of (h-x) -potential energy plus kinetic energy of 0.5m**v^2 when v equal to ωR. this energy also going for the rotation of the pulley E=0.5Iω^2. I suceeded by finding the height of h with those equations: h=x+m*L/mr-ω^2R^2/2g-m*ω^2R^2L/2mrg.
    but it doesnt helps me finding the relation between x and ω...
    I can`t find more equation, couldn`t think of an equation that link also the inertia of the "ring" of the wrapped rope....
     
  2. jcsd
  3. Feb 4, 2017 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    If h is not given, why introduce it? Can't you take it as zero?
    By the way, I think your energy equation is not quite right.
     
  4. Feb 4, 2017 #3
    how could I express potential energy without h? or the potential energy isn`t relevantic at all?
     
  5. Feb 4, 2017 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    maybe I misunderstood what your h is. I took it to be the initial length of the hanging rope. If it means the height of the pulley above the ground, its contribution to PE is constant. Just take the reference ground as the height of the centre of the pulley.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Pulley with a rope
Loading...