1. Limited time only! Sign up for a free 30min personal 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!

Falling Rope on a scale

  1. Jun 5, 2008 #1
    1. The problem statement, all variables and given/known data
    A uniform flexible rope is suspended above a scale, with the bottom of the rope just touching the scale (gravity points downward). The rope has a length L and a total mass of M. The mass is uniformly distributed along it's length.

    The rope is released. After a length x<L has fallen onto the scale, what does the scale read? Assume the scale can measure the force applied to it instantaneously. (Hint: the force exerted by the rope on the scale has two components).

    2. Relevant equations

    3. The attempt at a solution
    so p(t)=(M/L)*(v(t)^2)
    thus dp/dt=(M/L)*(g^2)*t^3

    also, x(t)=g(t^2)/2--> t=sqrt(2xg). plug that into the eqn for dp/dt, and get

    However, that solution doesn't treat the problem with a force of two components, nor do the units seem to work out. Any ideas?
  2. jcsd
  3. Jun 5, 2008 #2
    Let M=mass, L=length of the rope, v=velocity

    You have to express in component form,
    [tex]F_{net} + \frac{dm}{dt}v=m\frac{dv}{dt} [/tex]
    [tex]= F_{n} - mg+\frac{dm}{dt}v=0[/tex] (Eq 1), then

    [tex]\frac{dm}{dt}=\frac{-M}{L}v[/tex] (*), where dm=mass of the section of the rope that falls on the scale.

    Substitute (*) back into (Eq 1) and find v using [tex]v^2=v_{0}^2+2a\Delta y[/tex]
    Then find [tex]F_n[/tex]
  4. Jun 5, 2008 #3
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook