Finding final velocity given 2 charges

  1. 1. The problem statement, all variables and given/known data

    A small metal sphere, carrying a net charge of q_1 = -2.70 \mu C, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q_2 = -7.60 \mu C and mass 1.50 g, is projected toward q_{1}. When the two spheres are 0.800 \rm m apart, q_{2} is moving toward q_{1} with speed 22.0 \rm m/s . Assume that the two spheres can be treated as point charges.

    [​IMG]

    What is the speed of q2 when the spheres are 0.410 m apart?
    How close does q2 get to q1?


    2. Relevant equations

    F=k(Q1Q2)/r^2
    U=k(Q1Q2)/r




    3. The attempt at a solution

    I don't really know how to do this problem but i started it in this process-

    The potential energy is the work done in moving the charge through the electric field. That Potential energy is donated U. So i know that the work done in the system will equal a force x distance. F = ma. ( Work= Fd). so the U = ma x distance. Then using this i could find the acceleration and the velocity... problem is i have not time intervals. so im lost. please help
     
    Last edited: Sep 16, 2009
  2. jcsd
  3. rl.bhat

    rl.bhat 4,435
    Homework Helper

    What is required in the problem?
     
  4. kuruman

    kuruman 3,448
    Homework Helper
    Gold Member

    You don't say what the question is, but it looks like you need to use conservation of mechanical energy, time is not an issue here. KE + PE at one point is equal to KE + PE at another.
     
    Last edited: Sep 16, 2009
  5. so i need to find the electrical potential energy. Then this is equal to the KE= 1/2mv^2;

    so K(Q1Q2)/r=1/2mv^2 and solve for v at r .410m for the first question

    then how do i find how close they get to each other. Using the same equations and solving for r where ke=u? if so, how do i find v^2 for the KE?
     
  6. The kinetic energy of the charge q2 is zero at the point of closest approach since it is instantaneously at rest there.
     
  7. well i worked out part 1 of the problem and got 24.5m/s which is wrong. When finding the potential energy at the point .410, which lies between the 2 charges, do i use .410 for the distance r in the equation;

    U=(8.85e9)*(-2.6e-6 * -7.6e-6)/r = 1/2mv^2 ?
     
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