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!

Maximum force on rope and wavefunction

  1. Jul 2, 2016 #1
    1. The problem statement, all variables and given/known data
    A sinusoidal wave on a rope with linear density ##\mu=0.012 kg/m## is described in SI units by $$\xi(x,t)=A sin (kx-\omega t)= 0.15sin(0.8x-50t)$$
    a) find the maximum acceleration of a rope element
    b) find the maximum transverse force on a piece of rope ##1 cm## long
    c) Show how the force depends on the tension of the rope
    2. Relevant equations
    Wave equation

    3. The attempt at a solution
    a) This is simply ##a_{max}=\omega^2 A=375 m/s^2##
    b) This should be ##F_{max, y}=m a_{max}=\mu \cdot 0.01 \cdot \omega^2 A = 0.045 N##
    c) Tension should be related to such force by ##F_{y}=-T \frac{\partial \xi}{\partial x}## but here is the problem, since
    $$\frac{\partial \xi}{\partial x}=-0.12 sin(0.8x-50t) $$

    So the maximum value is ##0.12 ## and the force should be

    $$F_{max,y}= 0.12 T= 0.12 \cdot \mu \cdot v^2$$

    Now ##v=\frac{\omega}{k}=\frac{50}{0.8}=62.5 m/s## so it should be

    $$F_{max,y}=0.09 N$$

    Different from the value found in b), which is strange, did I get something wrong?
    Last edited: Jul 2, 2016
  2. jcsd
  3. Jul 2, 2016 #2
    I think I have a clue but I'm not sure... when you say that Fy= -T de/dx ...

    Isn't it Fy= -2T de/dx at the maximum point ? Since the tension acts on both sides of the rope element

    And the derivative of the sine is the cosine
    Last edited: Jul 2, 2016
  4. Jul 5, 2016 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In the equation F=ma, how exactly is F defined? Constrast that with tension in a rope.
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: Maximum force on rope and wavefunction