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Calculate the Effective Spring Constant using Coulomb's Law

  1. Apr 22, 2009 #1
    1. The problem statement, all variables and given/known data
    Consider a segment of a molecule of DNA that is a coil with an overall length of 2.1*10^-6 m. If the ends of the molecule become singly ionized (one end loosing a single electron and the other end gaining a single electron) the helical molecule acts like a spring and compresses by 1.08% of its original length. Determine the effective spring constant of the molecule.


    2. Relevant equations

    F(elec)= F(spring)
    ke* [(Q1*Q2)/r]= k*(change in r)


    3. The attempt at a solution
    The DNA will have a charge of +e and one end and -e at the other end which we will plug in for our Q1 and Q2 values.

    I'm particularly concerned if I calculated the radius and change in radius correctly:
    Calculate change in r:
    .0108*(2.1*10^-6 m)= 2.3*10^-8 m

    Calculate r:
    2.1*10^.6 m- 2.3*10^-8 m= 2.1 *10^-6 m
    It seems fishy that my r is the same as my r initial.

    Plug in to equation: ke* [(Q1*Q2)/r]= k*(change in r)
    8.99*10^9 Nm^2/C^2 *[(-1.60*10^-19C)*(+1.60*10^-19C)/ (2.1*10^-6 m)]= k*(2.1*10^-6 m)

    k= -4.76*10^-15
     
  2. jcsd
  3. Apr 23, 2009 #2

    Redbelly98

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    For the electrostatic force, it should be r2 rather than r.

    Note that r is known to about 5% accuracy, while the change in r is only about 1%. Or put another way, the 2.3*10-8 would affect the 2nd decimal place of 2.1*10-6, but we are only accurate to 1 decimal place there.

    Couple of errors being made here. The r2 I mentioned earlier. Also, shouldn't the change in r, 2.3*10-8 m enter in here somewhere?
     
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