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!

Homework Help: Rope Sag and Force on a Block Being Pulled

  1. Feb 17, 2009 #1
    1. The problem statement, all variables and given/known data
    A block of mass M is pulled along a horizontal frictionless surface by a
    rope of mass m, as shown. A horizontal force P is applied to one end of
    the rope. (a) Show that the rope must sag, even if only by an imperceptible
    amount. Then, assuming that the sag is negligible, find (b) the acceleration
    of the rope and block, (c) the force that the rope exerts on the block, and (d) the tension in
    the rope at its midpoint.

    2. Relevant equations

    3. The attempt at a solution
    To be honest I don't have a clue on where to start any segment of this problem... Especially part a and part d. Any help you guys can offer would be greatly appreciated. If you need to see the image I'm sure I could upload it somewhere (basically it's just a block M being pulled by a rope m in the right horizontal direction by some force P).
  2. jcsd
  3. Feb 17, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    A rope of mass m supported at two points not directly above each other will take the shape of a catenary curve and thus sag (the curved shape approximates a parabola for small sags). This can be shown by equilibrium equations in the vertical direction, where the downward weight must be offset by the vertical upward component of the wire tension (if the wire didn't sag, there would be no upward tension component). The acceleration of the rope and block can be determined from Newton 2 applied to the system; then to find the rope force at certain sections of the rope, take a free body of the rope at at those sections and apply Newton 2 again.
  4. Feb 17, 2009 #3
    Thanks for your help, I'm still kind of stuck on the rope sag though. Maybe if I could get some help on a free body diagram for the rope with mass? I have going to the right the Fpull, down Fgravity, and up a Fnormal. Not sure where on the free body diagram for the rope I would put Ftension though. Sorry if I'm being a bother, Physics is not my strong point at all.
  5. Feb 17, 2009 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Analyze a section of rope in the middle. What forces act on it? If there was no sag, what direction would the tension forces (from the rest of the rope) act? What's the sum of the vertical forces?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook