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: Tension on the rope (classical mechanics problem)

  1. May 3, 2017 #1
    1. The problem statement, all variables and given/known data
    The situation is that of Goldstein's problem 1.21 (or 1.19 in some editions):
    "Two mass points of mass m1 and m2 are connected by a string passing through
    a hole in a smooth table so that m1 rests on the table and m2 hangs suspended.
    Assume m2 moves only in a vertical line."
    But the question is the following: what is the tension?
    2. Relevant equations
    The Euler-Lagrange equations of the system are:
    $$ \frac{d}{dt}(m_1 d^2 \dot{\theta})=0$$
    $$ (m_1+m_2)\ddot{\theta}=-m_2 g+m_1 d \dot{\theta}^2$$
    The constraint equation is:
    Where ##l## is the length of the rope.
    3. The attempt at a solution
    I started by using the fact that the only force applied on ##m_1## is the tension, and that this tension must be in the direction of the string; that is, always radial (using the hole as the frame of reference). This means:
    $$F_{r_1}=\frac{a_{r_1}}{m_1}= \frac{\ddot{r_1}-r_1 \dot{\theta}^2}{m_1}=-T$$
    Where ##T## is negative because I define it as being positive when it is pulling up mass 2 (the other mass) such that:
    $$T=m_2 \ddot{r_1}+m_2 g$$
    Because ##\ddot{y_2}=\ddot{y_1}##
    I've been playing with all of these equations for a while, but I couldn't find the solution. I'm not sure if there is a way of obtaining an expresion ##T## that involves Lagrangian mechanics, or if there are any other techniques to do it.
    I'm following a problem set from a Classical Mechanics course I'm taking at college, and there is another question in the problem set: "In order to calculate the constraint forces on a system, what are the methods that could be employed?". I'm not sure how to answer that question, and I think that maybe some info on that (maybe some textbook that covers the subject?) may help me solve the problem. Thank you very much.
  2. jcsd
  3. May 4, 2017 #2


    User Avatar
    Science Advisor
    Gold Member

    There is very little maths needed to solve this problem .

    Draw free body diagrams for the two masses and just look at them .
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted