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Mass attached to a rope. the rope encounters a nail.

  1. Apr 16, 2016 #1
    1. The problem statement, all variables and given/known data
    M is attached to a rope L and starts from horizontal. the rope hits a nail at distance D.
    What is m's velocity when it reaches the lowest point.
    At what minimal distance D should the nail be places so that m will complete a circle round the nail.
    Snap2.jpg
    2. Relevant equations
    Kinetic energy: ##E_k=\frac{1}{2}mv^2##
    Potential energy: ##E_p=mgh##
    Centrifugal force: ##F=m\frac{v^2}{r}##

    3. The attempt at a solution
    Conservation of energy relative to the lowest point:
    $$mgL=\frac{1}{2}mv^2\;\rightarrow\; v=\sqrt{2gL}$$
    The centrifugal force at the top equals only the weight:
    $$m\frac{v_2^2}{L-D}=mg\;\rightarrow\;v_2^2=(L-D)g$$
    The kinetic energy at the bottom, which equals the initial potential energy, equals the potential and kinetic energy at the top:
    $$\frac{1}{2}mg(L-D)+2\cdot mg(L-D)=mgL\;\rightarrow\; D=\frac{3}{5}L$$
     
  2. jcsd
  3. Apr 16, 2016 #2

    ehild

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    Homework Helper
    Gold Member

    It looks correct.
     
  4. Apr 16, 2016 #3
    Thank you Ehild
     
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