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!

System with varying mass - String

  1. Oct 14, 2007 #1
    System with varying mass --- String

    A string of mass M and length L is placed near a hole on the top of a horizontal and smooth table. A slight disturbance is given to one end of the string at time t = 0 so that it leaves the table through the hole. Assume the string on the table remains at rest while the remaining part is moving down. Denote the length of the string under the table as y and the speed of the string that is moving down by v.

    Find:
    1. v as a function of y
    2. y as a function of t
    3. the velocity of string when the whole string leaves the table
    4. the time when the whole string leaves the table

    [ Use the D.E. dy/dx + y P(x) = Q(x) to solve the problem. ]

    I don't know how to do the first 2 questions. Please give me some ideas.
    ~ Thank you ~
    ----------------------------------------------
    Here is my idea:
    By considering the momentum
    Fext= M dv/dt + (v-u) dM/dt -----★
    (Resnick, Halliday--Physics 4th edt., Ch.9)
    Fext= Mg , u=0 (remaining part rest at table)
    dM/dt = ρdy/dt
    ∴ ★ becomes :
    dv/dt + v(1/L)dy/dt = g
     
    Last edited: Oct 14, 2007
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: System with varying mass - String
  1. Velocity of Mass (Replies: 0)

  2. Missing Mass (Replies: 0)

  3. Mass of helium (Replies: 0)

  4. Mass moments (Replies: 0)

  5. Pulley System (Replies: 0)

Loading...